When I first set out to get a game of The One Ring together, one of the first things I did was of course dream about how I could put Howard Shore's wonderful scores from the films to use in the games. I found our main theme, and set up playlists for battles, for sneaking around, for deep sorrow and great tension.
Then I started looking around for a way to stream it into the Google Hangouts session we would be playing in. I found some potential solutions, but aside from being overly complicated (SoundFlower; look it up), when I finally got it working, the sound quality was horrendous.
Then I looked at trying to use the YouTube extension for Google Hangouts; but aside from it having a horrible interface, it proved itself unworkable, as it would mute people's microphones, and play at uncontrollable volumes, not play in sync, and finally, interrupt the game with ads.
To make a long story, which played out over months, short. The answer is Nicecast (at least on OS X). It works perfectly, streams straight from iTunes with no fuzz and full volume control under the broadcaster's control. It's $60, and I highly recommend it.