If you like strategy: Starcraft 1 and Diablo 2 are pretty good multiplayer games (and they will run on just about any piece of crap computer you can find...)
If you like Shooters: Most of the Counter Strike games are good for Lan (off or online), Halo: Combat Evolved (pc), Half-life (the first one is good and runs on many different machines), arma is pretty good, SW:BF2 is good for co-op, Modern Warfare 2
If you like racing: Need for Speed Underground 2 and Hot Pursuit are off or online capable, Trackmania (free available) not that technical but fun