A good, relatively quick-playing space exploration-and-empire game was Yaquinto's Starfall. It doesn't have all of the details of some of the other games mentioned in this thread, but it does have a nice texture, and you can play it in an evening. The FTL travel mechanism is unusual, too: you go through a "starfall point" which instantaneously whisks you to another region in space. The twist from your usual "warp point" is that you arrive anywhere in a 6x6 hex sector, and there's no corresponding point at the other end. Thus, you can wind up on the other side of the galaxy with no way back. It makes for some interesting strategic decisions.

Of course, this game is long out of print. It doesn't show up very often on the auction circuit, either. On the other hand, when it does show up, it usually goes for a pretty low price. So keep an eye out for it.