Can you write with music playing?
I can’t.
My designer and photographer bretheren may be able do a day’s work with their iPods on, but I can’t write a lick that way.
I can listen. Or I can write. But not both. It’s like trying to shave with one hand while combing your hair with the other. One always suffers.

Part of the problem is the lyrics. When you’re trying to pick words out of a hat, it does no good to have someone crooning a stream of other words at you, in rhyme, no less. But even distinctive instrumentals — such as a drum solo by Ginger Baker or a Joplin piano rag — can pull my brain right out of a sentence.
We writers aren’t doomed to labor in silence, however. I stumbled on a few types of music compatible with writing copy.
I wrote a pile of case studies to the music of composer Philip Glass. You might call his work minimalist, or monotonous, depending on your point of view. Anyway, it doesn’t short-circuit my word-juggling. I like his Violin Concerto and his soundtrack to the movie Notes on a Scandal. The latter seems to help me increase the rpm when I’m on deadline.
Also useful is the Drone Zone from SomaFM. It’s more of an audio texture or an environment than music. It can, however, sometimes relax me into a stupor. Drone Zone is also streamable through the Radio feature of iTunes.
Try Sky.fm for their Solo Piano, Ambient, and New Age channels. Sky’s Simply Soundtracks is like being at the movies, but without the dialogue or pictures. I like Uptempo Jazz, but it can make me riff uncontrollably at times, with all sorts of asides and parenthetical comments. I have to cut them all out later.
Classic FM is helpful, except when it launches into opera or crashing symphonies. The station interrupts for commercials, but since they’re in Dutch or Czech, it’s the same as white noise to me.