Mark and Brian pretty much covered it. While you can get 'almost' any domain suffix, there are a few restrictions on some of them, so you'd need to follow those rules in order to be allowed to have those suffixes.

As for becoming popular, it really depends on the site itself, and not necessarily the suffix. A .uk is more likely to show up in UK specific searches, I think, but a similar .com address could just as easily show over there, so it really just depends.