There seems to be a bit of confusion on what the policy for playing music in the background for a gaming channel is.
Now I was under the impression that only channel owners in the Partnership Program were not allowed to play music on stream. However, now I'm getting word that might apply to all channel owners. At least that's what I'm hearing since a gaming channel I follow on TwitchTV was recently closed for 24 hours due to DMCA on music.
Then there's the whole issue of video games that already include copyright music within the game. An example is GTA IV and the radio stations while you play the game. A site like YouTube flags this sort of thing with a DMCA warning.
So for those new to streaming, it's probably for the best that you don't play licensed music on your stream. Besides, there's plenty of non-copyrighted music out there.