Is listening to music dangerous while cycling?
It is worth noting that deaf people cycle perfectly well.

@Joe's excellent comment merit's adding into the answer...
Edit It should also be noted that deaf people are used to being deaf. They never rely on sounds like hearing-abled people do. 

Its OK to listen to music as long as 


a) you are aware that you don't have any audio clues to hazards
b) don't put yourself in a situation where you rely on audio clues
c) you compensate with very alert visual monitoring of your environment.


That said, I don't listen to music while cycling.