In Fallout 3 you got a house. Do you get one in New Vegas? I haven't run across the quest line that grants you one.

I won't get into spoilers but I can say that I have 3 right now at about level 16. First one I got fairly early, but it also wasn't so great. Basically think about what kind of housing you'd expect to be staying at in Vegas and you'll figure it out fairly quickly.

Yes, several you can obtain.