You don't have to join one, but you get awesome stuff from them once you reach a certain rank or some such with them. But you can go total merc and just be like a gun for hire for all of them.

You need not even reach a rank with the specific factions. If this feature from the Alpha holds, you need only reach a certain rank in the Crucible. Which makes sense, since each faction will be playing a role in the Crucible.

That sounds awesome! Be all like, "I'm Commander Shepard, and this is my favorite store on the citadel." And just walk out with an arm load of sponsor gear ;)