Evolution (or EVO, for short) is the largest fighting game tournament in the world, and it happens once a year in Las Vegas. It's that time of the year again: this year's EVO will be on this weekend, starting Friday morning, with most games' final matches happening on Sunday. If you've never watched before, this is a great time to start!
You can watch the tournament from the two streams: SrkEvo1 and SrkEvo2. Capcom Pro Tour will broadcast all of the Ultra Street Fighter 4 pools through its official channel. The main games this year are Super Smash Bros. Melee, Injustice, Killer Instinct, Tekken Tag Tournament 2, Ultra Street Fighter IV, Ultimate Marvel vs. Capcom 3, King of Fighters XIII and Blazblue: Chrono Phantasma, with additional side tournaments happening for Skullgirls, Persona 4 Arena, Soul Calibur V and Super Street Fighter II Turbo.
Below is the full schedule (times in PDT / GMT - 7):

There will also be an additional stream by Madcatz, covering some of the numerous side-tournaments that always happen at EVO, as well as showing off various upcoming games, like Yatagarasu: Attack on Cataclysm and Persona 4 Arena: Ultimax.

Traditionally EVO includes several other events besides the main tournament, like guest panels and areas where developers bring preview builds of games still in development for players to test and give feedback on. This year, like the last, EVO is also raising funds to support a scholarship for a degree in Game Design at the NYU Game Center in New York. If you're interested, can find more info on how to contribute to that here: http://shoryuken.com/2014/07/08/stream-monstering-for-a-cause-support-the-2014-evo-scholarship/
Another thing that usually happens - a small thing, but one of my favorite parts of watching the finals on Sunday - are the community-created intros for each game, usually put together by independent artists and composers. These were the intros for some of last year's games:
Super Street Fighter 4: Arcade Edition 2012
Ultimate Marvel vs. Capcom 3
Persona 4 Arena
Super Smash Bros. Melee