I almost always listen to the radio with headphone on my commute and have never had a problem because of it. One morning however, my batteries went dead mid-ride so I road in in silence. As I was riding past some woods I heard a noise (probably would not have heard it if the radio was on) and was looking in the darkness for the cause, I didn't want a dog or deer to run out in front of me. Instead I hit a wheel sucking pothole (one of those long narrow ones that run parallel with your bike) and got a flat and went over the front of the bike. Would I have avoided the accident if the radio was on maybe, but I might have hit something coming out of the woods if there had been something.

Lesson learned: Don't zero in on one thing so much that you aren't paying attention to anything else.

I still listen to the morning talk radio show on my way to work