Unreal Tournament and I'll be willing to help out the tournaments by accepting any weapons or IG challenge!
RTS games would be excellant, but as Dink said they can drag out for a long time depending on who's playing who. If its me versus my brother, then its over in about 15minutes. I haven't been able to ever get close to beating him, but he's been beating kids in the dorms since the first warcraft was released.
Oh, and never underestimate the fun of a challenging Tetris competition!
You could also do challenges of 1-player games or simple platform games, just base the winner on score or best time of completion.