Currently the most popular of the MOBA games online, League of Legends, has started their world tournament. Day one is complete, with more games continuing this evening and continuing through the week. http://na.lolesports.com/ has all the details on what happens in the group stages.
When live, the games are normally streamed on http://twitch.tv
Competition in the MOBA space is coming, with SMITE, DC's Infinite Crisis, and other games in beta or in development.