Most people tend to be in one corner or the other on this situation - can you listen to music while you are working or studying? I used to be firmly in the no, not a chance, never corner. I would study and work in ideally complete silence. Then I started working in a rather noisy office environment without a quiet office policy and found myself incredibly distracted by all the noise. So, like many others in the office, I have turned to listening to music on my phone. iPhones are great like that!
One thing I must say is that I absolutely cannot listen to anything top 40 or too up beat, because I find myself singing along and so that is not only not good for my colleagues, but doesnt really help with my work. I find some of my most productive work is actually done listening to Bach. I have one classical album that I bought years ago to help with my study at uni and it honestly all sounds the same to me so I can use it to block out the distracting noise of chatter, but the music itself keeps me focused on work or study.
This did however get me thinking and I did some research and apparently introverts are more likely to be more productive with the less stimulation from their environment, where extroverts are better with a higher level of stimulation. However, the same study also showed this:
Furnham & Bradley (1997) showed that people who found music distracting while working are less likely to work with the radio on. Source
Listening to music when I am running or exercising however, that is a whole different story!