How can I play music while chatting in Google Hangouts? I want to play music while chatting in Google Hangouts and let both parties hear it, as well as our talking.

I'm using Apple earbuds with a built-in (external) mic on a MacBook Pro from about 2009.  Conversation works fine, and when I play iTunes or something in QuickTime, I hear it through the earbuds, but the person I'm talking to can't.

Enter Audio MIDI Setup, an Apple utility in OS 10.6.8 (in my case).  It lets me create an Aggregate Device, which can be used for input or output or both, but I can't find the magic combination to achieve the goal stated above.  Can Audio MIDI Setup do this?
What you need is an audio loopback.  Basically, what it does is it takes the output from one device and "loops it back" to the input of another device.  

You're in luck.  There's an App that does that and coincidentally, it's called "Loopback."

Macworld has a good article on it and apparently, it's rated quite high.