Warheads ( www.warheads.net )
If any of you have played Scorched Earth or Tank Wars or other games of that genre, you'll be familiar with the concept behind Warheads. It's turn-based, can be played over the Internet, and the idea is that you want to blow the other players up. You're sitting on a planet, and the other guys are sitting on other planets, and you must adjust the angle and initial velocity of your cannon so that your shot will hit the other person. You take a shot, the other guy takes a shot, you adjust your angle/velocity based on where the previous shot went and shoot again, the other guy does the same, etc. until someone gets killed.
Best game ever. Well, if you don't count Minesweeper and Stars!.
Doesn't require much in the way of system resources or bandwidth (ahem, Womble).