A friend recently told me that the newest release of the Civilization series (Civ IV) was reputed to be a great version of the game. I downloaded the demo (FilePlanet), tried it out, and think I'm addicted (even though the demo is limited to 100 turns). The last Civilization game I played was Civ II, and I'm happy to see that the game still has the same strategic focus (and has stayed turn-based, preventing it from becoming an RTS click-fest). It also looks like the game has more victory conditions, meaning that players no longer have to take over the world to win (as I seem to recall was functionally the case in Civ II).
Civilization Fanatics has a lot of information (and news) on the game, including a good overview of the changes to the game from earlier versions, and an HTML-based leader picker (which helps players choose what leader they want to be based on the leader characteristics they're looking for). They've also linked to the Blue Marble mod, which changes the in-game graphics so they better match satellite images of Earth (based on NASA's Blue Marble Project).
For those of you who've played earlier versions of the game, the Civ IV website has a historical comparison of the graphics in each version. And, if you're looking for more information about the game in general, the Wikipeida has good background information for the series on the Civilization page, as well as a detailed page on Civ IV.
If you see my posting frequency drop precipitously in the coming weeks, you'll know I've gotten a full copy of the game.