I'm a fan of RPGs, and my favourite would have to be Realmz. In terms of graphics and style though, TaskMaker/Tomb of the TaskMaker were the most impressive.
My favourite FPS for single play is split between Deus Ex and Marathon Infinity, and for network play is Unreal Tournament (the original, which let you have up to 4 teams, not just red vs blue!)
The best LAN party game was Bolo, which was way before it's time in terms of networking options and compatibility (from a Mac Plus up!)
Other highly esteemed games include Dark Castle, Spaceward Ho!, Scarab of RA, Gunshy, System's Twilight and Lord of Destruction.