Below is a list of game-important groups. This includes human organisations, both allied and hostile, as well as various beasts and aliens. The list will grow in time as canons are added and plot progresses.
NOTE: This is written from an in-character perspective, except for parts that player characters aren't supposed to know yet that are clearly marked as such. These organisations are NOT all common knowledge, especially the secret ones, though a member of Unity Group should have at least some idea what they are.
RAMPAGING MONSTERS
These creatures may be big or small, but usually they are very big, and very nasty. They are not sapient (though they may be sometimes be controlled by an evil overlord or mad scientist) and often leave a trail of destruction and animalistic fury wherever they go.

BETA
Swarming alien invaders with a hive-mind mentality. They come in many highly-specialized varieties, including anti-air lasers and melee combatants with ridiculously hard front armor. Their hives are rare, but are nigh impenetrable fortresses.
Canon: Muv Luv

Kaiju
Giant monsters that appear every so often from the Breach - a one-way rift in the middle of the Pacific Ocean floor. They deliberately target human cities on the coastline, always act alone but are notoriously hard to kill. Each Kaiju is different and has different abilities. Their blood, known as Kaiju Blue, is highly acidic and can severely contaminate the environment.
Canon: Pacific Rim

Noise
Strange creatures that have possibly plagued humanity for a long time, but appeared very infrequently. Their appearance intensified during the last years but statistically a person is expected to experience less than one Noise attack during their lifetime. Noise can shapeshift, slowly phase through solid matter, and turn unprotected humans into carbon just by touch. Unfortunately, most weapons seem ineffective against them so they are categorized as a natural disaster rather than humanity's enemy. After an influx of activity, Noise appearances dropped to previous, rare levels.
Canon: Symphogear
INVADING ALIENS
Organized threats to mankind that do not originate from Earth. The difference between aliens and monsters is that even if the latter have extraterrestial origins, the former are sapient (or at least seem to be) and have some kind of hierarchy or army. Still the lines can be sometimes blurred.
Anti-Earthling Party
Extremist group of Gebians (bug aliens who visited Earth a long time ago and were greatly inspired by ancient Egypt), focused on conquering Earth and enslaving it under Gebian rule. Unfortunately, most of their race supports them.
Canon: Swarms of Gods (OC)

Decepticons
Group of Transformers, robotic aliens from planet Cybertron, dedicated to conquering others and amassing power. Enemies of the Autobots.
Canon: Transformers
Kijin
Gigantic extra-dimensional humanoids, few in number but very powerful individually. They have waged a war against humanity in ancient past - but lost and were sealed away, reappearing only infrequently... until recently.
Canon: Hell's Embrace (OC)

Shura
Human-like aliens whose members value individual prowess and are highly trained in martial arts. Their presence on Earth is minimal and their current goal is unknown.
Canon: Super Robot Wars Compact 3

Wulgaru
Alien invaders that actively seek to push humanity's presence out of space via large scale warfare. Their vaguely biological units are not tough individually, but are very numerous and act in a coordinated army-like manner. They also wield powerful beam weaponry and some have energy shields. They are an offshoot of Protoculture and harvest other races related to them to prolong their failing lifespans.
Canon: Majestic Prince

Za Balmary Empire ("Aerogators")
Mysterious aliens who attack through the use of Cross Gates. They often have a nefarious purpose of abducting humans rather than killing them - this is because they are masters of creating clones, at least one of which has infiltrated Unity Group for a time (Ingram Plissken). They are human-like, suggesting a common ancestry. They have a habit of conquering other races and using their strongest soldiers as cloning material for their armies - and their eyes are on humanity now.
Canon: Super Robot Wars Original Generation

Zentradi
An aggressive alien race of giants. They have a strict military-like society and not much of a culture except for that. Their units are not impressive individually, but are very numerous. They are creations of an ancient race known as Protoculture (who are also humanity's distant ancestors), but rebelled against their own masters and now seek to destroy everything Protoculture-related.
Canon: Macross
HOSTILE HUMANS
Internal threats - groups of humans, sometimes small terrorist cells, sometimes whole nations, with goals that are mutually exclusive with our own. Many countries that are not members of Earth Sphere United Nations belong here, due to their less-than-enlightened self-interest or casual disregard for human rights.
Knights of Guiding Hand
A secret order that generally means well and is full of honorable and just people. They have a device known as Sidereal Tapestry that predicts the future, and one of its prophecies requires them to kill a young boy (Volya Alkaev). Because of that and Volya being under Unity Group's protection, they oppose us.
Canon: Dirge of Fate (OC)
New United Nations Earth

A rogue state that seeks to unite all of Earth under one world order. It is inspired by organisations that fought against the Space Revolutionary Army 15 years ago, but its influence is limited to more desolate regions of the planet. Not considered a legitimate government by most countries.
Canon: Gundam X

Vagans ("Unknown Enemy")
A group of humans who originate from an old colony on Mars, forgotten by almost everyone else. Their living conditions are poor and they blame the rest of humanity for it, and want to retake Earth - by force. They specialize in hit and run attacks, though their major strike force was defeated so it is not sure what their next course of action will be.
Canon: Gundam AGE
FRIENDLIES
These organisations are helpful, or at least non-hostile towards the Unity Group.

Autobots
Group of Transformers, robotic aliens from planet Cybertron, dedicated to peace and protection of other races (and themselves) from the evil Decepticons.
Canon: Transformers

Earth Sphere United Nations
An intergovernmental organisation created to promote cooperation between humanity's nations. As the name suggests, it consists of nations not only on Earth, but also in space - including colonies on Lagrange Points and the Moon. The organisation has only humanity's best interest in its mind but unfortunately not every country is a member. ESUN is not a "world government", member countries are still autonomous with their own governments.
Canon: SRWU
Global Defense Force
A coalition of several nations' space forces. Being an alliance of several organisations and not a single one, it is rife with internal politicking and struggles.
Canon: Majestic Prince
The Gloster Foundation
A secret organization dedicated to keeping the rogue Kijin in check. Their job became only more difficult in time, so they have decided to reveal themselves to and ally with the Unity Group.
Canon: Hell's Embrace (OC)

Graveyard/The Executors
An organisation dedicated to hunting down and fighting PRAYERs. A nebulous, secretive and generally untrustworthy group. They utilize Mistletoes - tiny fairy-like artificial beings that can synchronize with few chosen people and grant them abilities to fight PRAYERs effectively.
Canon: Hellsinker

Pan Pacific Defense Corps
An international alliance created to contain and combat Kaiju. Their weapon of choice are giant robots - Jaegers, housed and constructed in bases known as Shatterdomes. They are one of the first organisations to use mecha in combat, but they are currently in decline and only one of their Shatterdomes is operational.
Canon: Pacific Rim
Pro-Earthling Party
Group of Gebians believing that their race should coexist with humanity on equal terms and in peace. Unfortunately they are in the minority.
Canon: Swarms of Gods (OC)

Ravens' Nest
A paramilitary organisation that hires out mercenaries (called Ravens) and organizes Armored Core arena fights. Although it supposedly does not hire Ravens out to break any laws, Ravens' Nest works only as a mediator and does not regulate what a Raven can and cannot do. As a result it has a shady reputation. The discovery of truth behind the Nest's origins threw the organisation into chaos and disarray.
Canon: Armored Core
Solaris
A secret organisation that fought years ago to protect the world from various threats. It has since fallen financially but cooperates with the Unity Group to get back on its feet.
Canon: SolSavior (OC)

UN Spacy
The space military of ESUN, created for the explicit purpose of defending Earth from aliens. It controls the largest fleet in the Earth Sphere, though various countries have their own independent space forces.
Canon: Macross

Unity Group
Created by ESUN, it's an organisation not responding to any single country, established to defend humanity as a whole from threats external and internal. It has a loose structure and does not have a lot of military-like rigour, but somehow many one-of-a-kind pilots and machines are part of its ranks.
In short, it's us.
Canon: SRWU
DEFUNCT ORGANISATIONS
These organisations used to be around, but for one reason or another aren't anymore.
Divine Crusaders
A group established by Bian Zoldark with the purpose of uniting Earth under a common banner, to face and defeat alien invaders. Despite its noble goal it was hostile towards the Earth's governments who did not want to cooperate with it, and was eventually defeated. DC survivors often joined other military organisations, some even Unity Group.
Canon: SRW OG

Meganoids
Technically they are not aliens, but cyborgs created by a man - Souzou Haran, Banjou's father. Unfortunately they went rogue and homicidal, having killed everyone in the research station that was their birth place except Banjou himself. The Meganoid leadership was defeated and their base on Mars destroyed, and they are no longer a threat.
Canon: Daitarn 3

PRAYER
Mechanical monsters that appeared from Shafts - tower-like structures that could appear anywhere on Earth. PRAYERs wandered around randomly (mostly in unpopulated areas, luckily) and killed anything in their path. They specialized in bullet hell-style combat. If killed or the Shafts are destroyed, they were reborn, and rather quickly to that. With the destruction of the Cardinal Shaft, all other Shafts were merely reflections of, the PRAYERs are gone for good.
Canon: Hellsinker
United Colony Corps
A space colonies self-defense force that decided to unite with DC and thus were defeated along them. Following the defeat, UCC was disbanded and most of its personnel became parts of UN Spacy and other assorted organisations (such as the Unity Group).
Canon: SRW OG
United Nations Earth
An alliance of Earthbound countries that opposed SRA's rise to independence 15 years ago. The war between the two was interrupted by alien and monster invasions intensifying in scope, and subsequently UNE was disbanded, with NUNE as its pale imitator.
Canon: Gundam X
Space Revolutionary Army

Government created by a group of colonies that waged a war of independence against Earth 15 years ago. It steadily lost influence over the years and only some mobile suit designs remain as SRA's legacy.
Canon: Gundam X
The Lady's Good Men
Cult devoted to the Lady, whomever she may be. The Lady blesses them with gifts, and they are enemies of people who they perceive to "abuse" such boons. The Lady's gifts all originate from an ancient installation discovered by Professor Dupond (this includes TSEN which is a replication of technology found there), and the cult was created by Dupond's assistant Aaron Anso Antema. With its leadership slain or captured, the Lady's Good Men are no more.
Canon: SRWU
NOTE: This is written from an in-character perspective, except for parts that player characters aren't supposed to know yet that are clearly marked as such. These organisations are NOT all common knowledge, especially the secret ones, though a member of Unity Group should have at least some idea what they are.
RAMPAGING MONSTERS
These creatures may be big or small, but usually they are very big, and very nasty. They are not sapient (though they may be sometimes be controlled by an evil overlord or mad scientist) and often leave a trail of destruction and animalistic fury wherever they go.

BETA
Swarming alien invaders with a hive-mind mentality. They come in many highly-specialized varieties, including anti-air lasers and melee combatants with ridiculously hard front armor. Their hives are rare, but are nigh impenetrable fortresses.
Canon: Muv Luv

Kaiju
Giant monsters that appear every so often from the Breach - a one-way rift in the middle of the Pacific Ocean floor. They deliberately target human cities on the coastline, always act alone but are notoriously hard to kill. Each Kaiju is different and has different abilities. Their blood, known as Kaiju Blue, is highly acidic and can severely contaminate the environment.
Canon: Pacific Rim

Noise
Strange creatures that have possibly plagued humanity for a long time, but appeared very infrequently. Their appearance intensified during the last years but statistically a person is expected to experience less than one Noise attack during their lifetime. Noise can shapeshift, slowly phase through solid matter, and turn unprotected humans into carbon just by touch. Unfortunately, most weapons seem ineffective against them so they are categorized as a natural disaster rather than humanity's enemy. After an influx of activity, Noise appearances dropped to previous, rare levels.
Canon: Symphogear
INVADING ALIENS
Organized threats to mankind that do not originate from Earth. The difference between aliens and monsters is that even if the latter have extraterrestial origins, the former are sapient (or at least seem to be) and have some kind of hierarchy or army. Still the lines can be sometimes blurred.
Anti-Earthling Party
Extremist group of Gebians (bug aliens who visited Earth a long time ago and were greatly inspired by ancient Egypt), focused on conquering Earth and enslaving it under Gebian rule. Unfortunately, most of their race supports them.
Canon: Swarms of Gods (OC)

Decepticons
Group of Transformers, robotic aliens from planet Cybertron, dedicated to conquering others and amassing power. Enemies of the Autobots.
Canon: Transformers
Kijin
Gigantic extra-dimensional humanoids, few in number but very powerful individually. They have waged a war against humanity in ancient past - but lost and were sealed away, reappearing only infrequently... until recently.
Canon: Hell's Embrace (OC)

Shura
Human-like aliens whose members value individual prowess and are highly trained in martial arts. Their presence on Earth is minimal and their current goal is unknown.
Canon: Super Robot Wars Compact 3

Wulgaru
Alien invaders that actively seek to push humanity's presence out of space via large scale warfare. Their vaguely biological units are not tough individually, but are very numerous and act in a coordinated army-like manner. They also wield powerful beam weaponry and some have energy shields. They are an offshoot of Protoculture and harvest other races related to them to prolong their failing lifespans.
Canon: Majestic Prince

Za Balmary Empire ("Aerogators")
Mysterious aliens who attack through the use of Cross Gates. They often have a nefarious purpose of abducting humans rather than killing them - this is because they are masters of creating clones, at least one of which has infiltrated Unity Group for a time (Ingram Plissken). They are human-like, suggesting a common ancestry. They have a habit of conquering other races and using their strongest soldiers as cloning material for their armies - and their eyes are on humanity now.
Canon: Super Robot Wars Original Generation

Zentradi
An aggressive alien race of giants. They have a strict military-like society and not much of a culture except for that. Their units are not impressive individually, but are very numerous. They are creations of an ancient race known as Protoculture (who are also humanity's distant ancestors), but rebelled against their own masters and now seek to destroy everything Protoculture-related.
Canon: Macross
HOSTILE HUMANS
Internal threats - groups of humans, sometimes small terrorist cells, sometimes whole nations, with goals that are mutually exclusive with our own. Many countries that are not members of Earth Sphere United Nations belong here, due to their less-than-enlightened self-interest or casual disregard for human rights.
Knights of Guiding Hand
A secret order that generally means well and is full of honorable and just people. They have a device known as Sidereal Tapestry that predicts the future, and one of its prophecies requires them to kill a young boy (Volya Alkaev). Because of that and Volya being under Unity Group's protection, they oppose us.
Canon: Dirge of Fate (OC)
New United Nations Earth

A rogue state that seeks to unite all of Earth under one world order. It is inspired by organisations that fought against the Space Revolutionary Army 15 years ago, but its influence is limited to more desolate regions of the planet. Not considered a legitimate government by most countries.
Canon: Gundam X

Vagans ("Unknown Enemy")
A group of humans who originate from an old colony on Mars, forgotten by almost everyone else. Their living conditions are poor and they blame the rest of humanity for it, and want to retake Earth - by force. They specialize in hit and run attacks, though their major strike force was defeated so it is not sure what their next course of action will be.
Canon: Gundam AGE
FRIENDLIES
These organisations are helpful, or at least non-hostile towards the Unity Group.

Autobots
Group of Transformers, robotic aliens from planet Cybertron, dedicated to peace and protection of other races (and themselves) from the evil Decepticons.
Canon: Transformers
Earth Sphere United Nations
An intergovernmental organisation created to promote cooperation between humanity's nations. As the name suggests, it consists of nations not only on Earth, but also in space - including colonies on Lagrange Points and the Moon. The organisation has only humanity's best interest in its mind but unfortunately not every country is a member. ESUN is not a "world government", member countries are still autonomous with their own governments.
Canon: SRWU
Global Defense Force
A coalition of several nations' space forces. Being an alliance of several organisations and not a single one, it is rife with internal politicking and struggles.
Canon: Majestic Prince
The Gloster Foundation
A secret organization dedicated to keeping the rogue Kijin in check. Their job became only more difficult in time, so they have decided to reveal themselves to and ally with the Unity Group.
Canon: Hell's Embrace (OC)

Graveyard/The Executors
An organisation dedicated to hunting down and fighting PRAYERs. A nebulous, secretive and generally untrustworthy group. They utilize Mistletoes - tiny fairy-like artificial beings that can synchronize with few chosen people and grant them abilities to fight PRAYERs effectively.
Canon: Hellsinker

Pan Pacific Defense Corps
An international alliance created to contain and combat Kaiju. Their weapon of choice are giant robots - Jaegers, housed and constructed in bases known as Shatterdomes. They are one of the first organisations to use mecha in combat, but they are currently in decline and only one of their Shatterdomes is operational.
Canon: Pacific Rim
Pro-Earthling Party
Group of Gebians believing that their race should coexist with humanity on equal terms and in peace. Unfortunately they are in the minority.
Canon: Swarms of Gods (OC)

Ravens' Nest
A paramilitary organisation that hires out mercenaries (called Ravens) and organizes Armored Core arena fights. Although it supposedly does not hire Ravens out to break any laws, Ravens' Nest works only as a mediator and does not regulate what a Raven can and cannot do. As a result it has a shady reputation. The discovery of truth behind the Nest's origins threw the organisation into chaos and disarray.
Canon: Armored Core
Solaris
A secret organisation that fought years ago to protect the world from various threats. It has since fallen financially but cooperates with the Unity Group to get back on its feet.
Canon: SolSavior (OC)

UN Spacy
The space military of ESUN, created for the explicit purpose of defending Earth from aliens. It controls the largest fleet in the Earth Sphere, though various countries have their own independent space forces.
Canon: Macross

Unity Group
Created by ESUN, it's an organisation not responding to any single country, established to defend humanity as a whole from threats external and internal. It has a loose structure and does not have a lot of military-like rigour, but somehow many one-of-a-kind pilots and machines are part of its ranks.
In short, it's us.
Canon: SRWU
DEFUNCT ORGANISATIONS
These organisations used to be around, but for one reason or another aren't anymore.
Divine Crusaders
A group established by Bian Zoldark with the purpose of uniting Earth under a common banner, to face and defeat alien invaders. Despite its noble goal it was hostile towards the Earth's governments who did not want to cooperate with it, and was eventually defeated. DC survivors often joined other military organisations, some even Unity Group.
Canon: SRW OG

Meganoids
Technically they are not aliens, but cyborgs created by a man - Souzou Haran, Banjou's father. Unfortunately they went rogue and homicidal, having killed everyone in the research station that was their birth place except Banjou himself. The Meganoid leadership was defeated and their base on Mars destroyed, and they are no longer a threat.
Canon: Daitarn 3

PRAYER
Mechanical monsters that appeared from Shafts - tower-like structures that could appear anywhere on Earth. PRAYERs wandered around randomly (mostly in unpopulated areas, luckily) and killed anything in their path. They specialized in bullet hell-style combat. If killed or the Shafts are destroyed, they were reborn, and rather quickly to that. With the destruction of the Cardinal Shaft, all other Shafts were merely reflections of, the PRAYERs are gone for good.
Canon: Hellsinker
United Colony Corps
A space colonies self-defense force that decided to unite with DC and thus were defeated along them. Following the defeat, UCC was disbanded and most of its personnel became parts of UN Spacy and other assorted organisations (such as the Unity Group).
Canon: SRW OG
United Nations Earth
An alliance of Earthbound countries that opposed SRA's rise to independence 15 years ago. The war between the two was interrupted by alien and monster invasions intensifying in scope, and subsequently UNE was disbanded, with NUNE as its pale imitator.
Canon: Gundam X
Space Revolutionary Army

Government created by a group of colonies that waged a war of independence against Earth 15 years ago. It steadily lost influence over the years and only some mobile suit designs remain as SRA's legacy.
Canon: Gundam X
The Lady's Good Men
Cult devoted to the Lady, whomever she may be. The Lady blesses them with gifts, and they are enemies of people who they perceive to "abuse" such boons. The Lady's gifts all originate from an ancient installation discovered by Professor Dupond (this includes TSEN which is a replication of technology found there), and the cult was created by Dupond's assistant Aaron Anso Antema. With its leadership slain or captured, the Lady's Good Men are no more.
Canon: SRWU