Diablo 2 is a good game, if you like atmosphere and hack-and-slashing. It's kinda like WoW, where you sometimes stumble across a really good item, which can vindicate the hours wasted (in a good way) on the computer screen.
Divine Divinity (The original, not 2) is like Diablo, but with a better story and more difficult and tactical gameplay. Dungeon Siege is basically a very good Diablo 2 clone, with a rather unique setting. Nox is also a Diablo clone, but also has a great setting.
By Diablo 'clone,' I mean in terms of gameplay, not story or anything like that. It's actually great since Diablo 1 and 2 had a great gameplay system anyway.
This isn't really a classic, but the game Torchlight is also very good. Again, it rips off Diablo 2, but is in a steampunk-ish and cartoonized setting. The game is made to run on basically any computer, and works on archaic Pentium 2 processors.
Deus Ex is also great, but it hasn't necessarily aged well. Still amazing if you like conspiracy theories, though, and you can play it almost any way you want. Wanna play it guns blazing? Check. Wanna play it as a sneaky bastard? check.
EDIT: The original Medieval: Total War is great in how it makes history go completely crazy, and has a great tactical battle system as well. Basically, you pick a country, build up your army and cities, and wage war on whoever you want. You can really conquer all of the Old World, if you happen to be godly at the game.