Listening to music while trying to think is distracting and decreases productivity. If critical thinking is not needed, and the task is repetitive and mundane, listening to music is still distracting but may help the time go by.
In a collaborative work environment headphones can be a nuisance and get in the way of communication. On a production floor or a job site that may have hazards headphones are not recommended.
As far as policy goes, we don't ban headphones but we prefer our employees use them judiciously and only when safe and their use does not compromise production.
I do not listen to music when actively engaged in my work. I find it distracting and counter-productive. In our shop I need to hear what is going on and be 100% available for comments and discussions with fellow workers.
Note that I am a musician and an audiophile; music is a big part of my life. There is a place and time for listening to music, but not when I am trying to figure things out or get things done.
