Since these three haven't been mentioned, I'll throw them out there:
Galactic Civilizations II: An old favourite of mine, as you can tell a interstellar empire game. It is turn based, and really low on the micromanagement; I think it's an easy one to get a hang of. It's AI is generally well designed, as well. Oh, and did I mention you get to design your own ships? If you do buy, try to make sure you get the second expansion pack, Twilight of The Arnor; the expansion packs add so much to the game.
Master of Orion II: The spiritual predessessor of the one above. It is much in the same vein as GalCiv, only from a different perspective; in this case, it's not, how do I describe it, on a Civilization-esque board like GalCiv; instead, you always see the galaxy as a whole, akin to always playing on what might otherwise be a mini-map. Harder to get into, and older, but a classic, so you might wish to try it later.
Sid Meier's Alpha Centauri: (Though it's more Brian Reynold's Alpha Centauri); The dark horse, and one of the best, of the Civilization series. Based on CivII's engine, it answers the question of "What happens when your CivSpaceship reaches the Alpha Centauri binary/trinary system?" with a, by turns, dark, fun, interesting, and eventually mind screwy answer. The UI is a bit clunky, and, because of its engine, unit movements in relation to one another are wierdly ruled, but another true classic, and is so interesting, engaging, and fun. You will not expect anything that happens in this game from the moment you start playing, the factions are interesting and clearly defined/different from one another, and gameplay... that's part of the surprise.