Actually, I'm gonna have to step in here and make a minor correction to the statement above me.Hey there!
Well, yes and no. There are three main factions to pick from: the Republic, the Jedi Order, and the Sith. You can only pick one, and stick with said faction. However, that doesn't mean you must stick to that faction and that faction alone with the rest of your characters. Any character is more than welcome to become an independent, or "Indie," which doesn't apply to really any main faction.
For example, if you join the Jedi Order. You can have two Jedi Knights, and then you can have an anti-Jedi bounty hunter or smuggler.
Hope that helps.