Pretty much all of Valve's multiplayer games, like Counter-Strike, Team Fortress 2, and Left 4 Dead. Online shooters just aren't my thing, but if I were to start playing one, it'd be one of those three.
There's also most point and click adventure games. I love games with good writing, and adventure games generally excel in that area, but whenever I try to play one I always end up having to consult a walkthrough one too many times for my taste and giving up. I'm sure games like Monkey Island, Day of the Tentacle, and Grim Fandango are all perfectly wonderful, but I'll still probably never play them because I just don't have the patience for it.