Other people have said it, but I would also recommend Call of Duty 4. It has levels and unlockable guns and abilities, so you have something to play towards, which keeps things interesting. But even if it didn't have unlocks the gameplay it self is really great as well. Fun, fast paced, great maps (some of them, of course), cool guns. Oh, and knives are fun too.
Also, and this one hasn't been mentioned yet, I think, Company of Heroes is a really fun RTS which has really epic, dramatic gameplay, especially multiplayer. You could do 2v2, or 4 humans versus 4 bots, either way it feels really dramatic. It's one of my very favorite RTS's, and plays rather unique, too. I think there are demos kicking around on teh internets, so you could try it out if it sounds interesting.
Other RTS's that are good multiplayer are Command and Conquer 3 (fast, fun gameplay, but less depth, in my opinion), Dawn of War series (very fun, but with unit caps that seem to limit the strategic choices to aiming for a few of the super units), Supreme Commander can be fun if you're into long, drawn out games, and, duh, STARCRAFT, as it is still fun, and a classic, if you want to play such an old game. Also, as other people have mentioned, Warcraft 3 has many, many custom maps and offers great variety. You can also get it for around ten dollars now.
Also, I agree with the people who have said Team Fortress 2 is really fun, although in my opinion CoD4 offers more variety.
And Diablo II and Hellgate: London can be fun, although I'd say the multiplayer isn't as deep as the other games, as they are essentially single player story/quest games with other players. Not to say they aren't fun, though, just different.
To conclude my long-ass rant, I would mainly recommend, in this order, Call of Duty 4, Company of Heroes, Warcraft 3, and maybe Diablo II.