Starcraft, the Homeworlds, Age of Empires 1-2 (not 3), the Earth series, the Battlezones, Empire Earth, Hegemonia, Empire at War, Rebellion, Warzone 2100…
Pretty much anything but Warcraft <_>
I think an RTS tournament would be a good addition to a LAN event. The only downside is that some of these games can take hours to finish so participants may have to pick between an RTS or multiple FPS.