I usually play MMORPGs, WoW to be more specific, they are great fun. I think the RTS games you listed are more FPS, which I play alot, CS and HL2 are great!
I am an old school FPS fanatic at my core. I will play pretty much any game in any genre but at the end of the day I feel most comfortable playing Quake, Unreal Tournament or Halo. Online is the only way to play!
One of my favorite computer games of all time is StarCraft so I voted war-based strategy games. I also like the Tycoon games, so some non-war based strategy, and some Flight Simulaters too.