In Fallout 3 the factions are organizations vying for control in the world of the game. Factions will offer you help and quests, but you will not be able to join any of them.GameFAQs: Fallout 3 Joining Factions Thread

There are five factions in Fallout 3 each with their own unique story and background.

1. The Brotherhood of Steel: The Brotherhood of Steel is a religious group that worships technology and one of the major factions in Fallout 3. They send an envoy to Washington D.C. to uncover any technology leftover from the wastes of the Pentagon and to worship reports of space mutant activity. The armor-clad soldier seen in Fallout 3's promotional art and front cover is a Brotherhood of Steel member.
2. The Enclave: The Enclave is the remaining arm of what used to be the United States government. They possess advanced technology and are the other big faction in the Fallout 3 universe.
3. Talon Mercenaries: A new faction with a military background.
4. Raiders: Groups of thieves and bandits wandering around the DC area wielding low-tech weaponry and showing little to no organizational structure.
5. Reilly's Rangers: A mercenary group led by a woman named Reilly and located at the Ranger's Compound.