I love listening to music when doing the easy parts of an application, like crud code, light refactoring, etc. If I have to really think about something, I find myself having to turn down the music, as it becomes distracting.
I find different types of music helps me with different types of work. For example, if I already understand a problem very clearly and have visualized most of the code in my head (and it's just a matter of typing it in), I like stuff with a very fast tempo - tends to be electronic.
However, if I'm just beginning to work through understanding a problem, sketching solutions or writing notes on my notepad, I like something very dynamic with lots of structure and intricacy - usually ends up being classical music, with an emphasis on piano concerti.
The only time I need absolute silence is composing e-mails or that sort of thing. Somehow forming sentences or otherwise writing in good, concise, coherent english requires a part of my brain that typically is free to listen to music. Maybe something to do with verbal/aural understanding.
Agree on the dual monitor neccessity.