Below I've listed links to the most popular @ E3 live streams.

Press

http://e3.gamespot.com/live-show/
http://e3.gamespot.com/live-show-2/
http://www.twitch.tv/gamespot (different footage from the main website streams)
http://www.twitch.tv/e3
http://ign.com/events/e3/2012/live-video

Esports

http://www.gamespot.com/e3mlg
http://www.twitch.tv/mlg_live

Individual press

http://www.twitch.tv/totalbiscuit