Civ IV >>> Civ V. You should really try it despite owning Civ V already. There's a demo available in case you're interested.
Total War series if you care for strategy games. Rome is possibly the best game in the series, but the recently released Shogun 2 is also one of the better games. There's a demo for at least Shogun 2.
The first Crysis is pretty awesome. You won't find a great story there but you'll find a great shooter with open environments and quite much freedom in what you do. Also, the nano suit is pretty fun.
I recommend trying Enemy Territory: Quake Wars if you care for multiplayer. It's not exactly exclusive but the PC version is far superior and the console versions never got that popular I think. The PC version doesn't have a huge player base either but you should never have trouble finding a server with enough players on it. Or you can try the free Wolfenstein: Enemy Territory which, while quite old already, is still very much alive and great. They're quite similar but they do have some differences as well.
Titan Quest is a Diablo clone. Some hate it, some love it. Personally I find it great, and there's a demo available. Of course Diablo II is still alive and shouldn't cost that much either...
Supreme Commander is definitely worth trying if you like strategy games. Huuuge scale battles, all in real-time. There's a demo for the game.
Deus Ex is already quite old but you should definitely try it. There's a PS2 version but... If you haven't played it, you should really try out the PC version. No, seriously. Try it. There's a reason why its has such good reputation.
Another must-try classic is Baldur's Gate II. You've probably heard of it and if you haven't, you should be ashamed. There's a demo for this one, too. The first game is pretty good too but BG2 is what you should try if you want something truly awesome.
Some other classic RPGs would be Planescape: Torment, the first Fallout games, Arcanum, and if you like combat in Baldur's Gate II, the Icewind Dale series might be good for you.
Then there's tons of adventure games. I don't really have much experience with them (I really don't have enough time for all the games I own), but The Longest Journey is supposedly quite good and decent-looking even now.
Operation Flashpoint is a must-try if you like war games/shooters. It's quite realistic but it's not that hard to get into if you dive into it with an open mind.
In case you like city building, I have a recommendation. Well, an old game but anyway. Emperor: Rise of the Middle Kingdom is quite fun. It's set in China from its foundation to the 17th century or so. It's in the same series as Zeus and Pharaoh and such.
Yeah, I think that's pretty much it. There's probably tons of games I missed but there should be something for you here - probably for a longer while too. Have fun with your choice(s)!