There's WCG which was the premier game tournament for a few years.
The biggest game-sports have ever made it was Starcraft 1 in Korea. The top players are paid $200,000+, the teams hve huge sponsors for millions of dollars, and the games are broadcast on live Korean television (OnGameNet and formerly MBCGame). It was Korea's fourth biggest real sport and the best players' names were known by everyone in the country.
The biggest game sports right now internationally are Starcraft 2 (was on live Swedish television and they have a deal with CBS), League of Legends and DOTA 2. Events happen nearly every weekend with prizes of $20-100k.
For example last week was Major League Gaming's Raleigh championship with >400 players in SC2 and LoL and >$150k in prizes.
http://www.majorleaguegaming.com/
