Ah one of the age old controversies...
It is my personal opinion that wearing headphones while riding a bike is dangerous and inadvisable. I firmly believe that simply plugging your ears (even if you keep the volume pretty low) takes your mind to a different place. It's not just the music.... its the earphones. In this state using headphones in a car is illegal - while certainly listening to the radio is not.
Some people will argue that headphones actually help them concentrate - so they like to use them to study etc. and that is why they feel safe riding with them. Actually, I totally believe that - and IMHO it backs up why I feel the totally opposite way. The headphones *do* help them in that manner. They allow the person to block out their surroundings and focus of the task of studying. Cycling, on the other hand, you need to have an acute awareness of all of your surroundings and be monitoring many things all of the time. Having good focus is not what you want. You need to be able to hear and process a great amount and I think headphones cut down on a person's ability to do both of those things.