Strategy:
Age of Empires I and II are always fun.
Empire Earth I on LAN is awesome! Beating up your prehistoric enemy with nukes never gets boring. Campaign is quite good too.

FPS:
Quake II, fastest death matches ever.
Battlefield 2, not that old (2005-ish) but still doesn't need that good of a computer.

Simulation:
Zoo Empire, Underrated.
<forget the name, 3D jurassic park or something>, Made in 2003, and is still worth playing
H.A.W.X, I know this only just came out, but it's the only modern game my computer has ever been able to play on high.