I'm going to have to go with Counter Strike.
The skill gap is like the Pacific Ocean, and it really shows off when you improve your game a lot. It's incredibly challenging playing against other skilled players, and extremely rewarding when you win with good tactics and good communication.
IMO, there is no game out there that reaches CS's height in competitiveness.
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Counter Strike? lol I didn't even read the OP and that's what I guessed. Outside of that, maybe StarCraft. Sad thing about those games is Blizzard's multiplayer team caters almost exclusively to the uber-competitive players there.