Operation Meteor - A group of colonists who originally wished to take control of the Earth. This group eventually became the Gundam Project, and its plans were never fully executed.
The Gundam Project - A group of colonists who decided to overthrow OZ and free the colonies from oppression using advanced mobile suit technology called "Gundam".
The United Earth Sphere Alliance, The Alliance - The military organization that was in power before OZ took over. It was located on both the colonies and the Earth, and OZ was a part of the Alliance... but the Alliance was overthrown by OZ early in the series.
OZ - A secret military organization that originated from the Romefeller Foundation, and wishes to supress the colonies. It started as a part of the Alliance until it overthrew the Alliance and took over completely. OZ's leader is Treize Kushrenada.
The Specials - A group of elite soldiers within the OZ. These fighters are so talented that they have the power to act whenever they wish, however they wish. They are based out of the Romefeller Foundation and serve as a cover in order to infilterate the Alliance Military.
The Romefeller Foundation - A group of wealthy European aristocrats who finacially back OZ and its operations. They place a huge importance on tradition.
The Treize Faction - A collection of soldiers who were once with OZ, but after Treize backed out of Romefeller, they followed him and became rebel fighters in hopes of putting Treize back in leadership.
The Sanc Kingdom - A pacifist European nation overthrown by the Alliance before the anime began. The entire royal family, except for Prince Milliardo and Princess Relena Peacecraft, were murdered. Later, the kingdom is rebuilt to represent Relena's ideas of pacifism, but doesn't last long.
White Fang - A rebel organization that orginated on the colonies late in the series with the hope of overthrowing OZ and taking control, thus cutting off all ties between the colonies and the Earth.
The Maguanac Corps - A group of 40 Arabian men who were once Space Hijackers and special mobile suit pilots. After meeting with Quatre Winner, and after he helped them in a battle, these men pledged their alligance to him and refer to him as their "Master". They are extremely loyal and will help Quatre in any way possible - and they'll help anyone he considers a friend.
The Earth's Sphere Unified Nation - An organization that was created at the end of the first war in AC 195. It exsists because the colonies and the Earth agreed to try and live in peace together, and it acknowledges the needs of both.
The Preventers - Another group created at the end of the first war in AC 195. The Preventors work to put down any small "fires" and rebel organizations that might try to repeat the history of war. They are comprised of former soldiers who fought both for OZ and other organizations.
The Barton Foundation - An organization that appears in the Gundam Wing OAV, Endless Waltz. This group was directly behind the original Operation Meteor. They wish to execute their plan and take total control of the Earth in AC 196.