In my case I cannot study with music at all. If I have any distraction that seems more appealing than studying, I concentrate on that distraction. I try to listen to music and study but the only thing I end up studying is the song. When I am in the library the constant noise of typing, rustling, and bustling do not even grab my attention. It makes me focus on my work as I do not care what other people are doing. Music, however, I do care about, therefore I cannot do both study and listen to music.

I've probably been one of those people mentioned. I might just be strange, but I find having a distraction like music keeps me focused on the task at hand. Paradoxical, but allow me to explain.

There are several reasons for why I think this way.
1) When you're not listening to music in a silent library, you hear everything else around you: chairs squeaking, people squirming, papers rustling. It's just creepy.
2) Classical music does indeed stimulate the brain. They're not kidding when they say Bach and Beethoven are good for studying.
3) Silence can be the biggest distraction of all. You feel the urge to turn and look at every little noise, instead of staring at the inhumanly dull research topic in front of you.

These, of course, are only personal reasons, though the 2nd one I believe has actually been clinically tested. I have to admit that there are some flaws in my system. For example, if the shuffle lands on my favorite song, staring at that paper doesn't happen again until the end of it.

One last thing. I've also noticed that the music turns into a muted buzz almost once you actually start concentrating. It has been one of my most fundamental checks during studying. If I hear the music, I'm not concentrating hard enough.