The NCR is considered the "Good" faction in the game. They are kind of like the New government in the West.
Caesar's legion
These guys are considered the "bad" guys. They are a group of 34 tribes collected by Caesar(their leader). They do horrible things to people to gain power and influence.
Important Subfactions
Brotherhood of steel
The brotherhood is a group of people who enjoy advanced technologies from the old world. If you help them they will help you in
Boomers
The boomers are a group of vault dwellers that found an abandoned military air base. They have massive artillery cannons they can use to help you at the end of the game.
The Strip
Mr. House is the leader of the strip and you can side with him at the end of the game if you help him enough. He has an army of robots that are under his command as well.
Followers of the apocalyse
The followers are a group who try to help the unfortunate people of the wastes. In the end of the game, they can provide medical help to injured people.