I very rarely run while listening to music. For me, running is very much a meditative activity, and listening to music only distracts me. And yet I am one of those people who, on some level, always has some music playing in the back of his brain, and this is especially true of running. So I guess in some sense, I do "listen" to music while I run.
The idea that music is part of what makes us human is fascinating to me. And so I found this link to a series of videos from the World Science Festival very interesting. It features a panel of neuroscientists who study music and the brain, with special guest Bobby McFerrin. If you're at all interested in the science of music, or if you just want to hear some very cool performances by a very, very talented musician, I highly recommend clicking through.