I had a thread awhile back, "Could you write to this" and mentioned I can only focus with loud chaotic music, Cradle of Filth was the example I linked.
But I can listen to slower beats, but they have to be heavy and when I'm setting out to write something 'vicious" I have an entire playlist of songs that are good at keeping that mood going.
On another side, when I have set out to write something that's going to be emotional or depressing I'll go with things like Seether's "Love her" Springsteen's song "The River" Snuff by slipknot...that type of stuff
When I'm in the mode of just writing fun sexy stuff, I enjoy do wop, great beats, fun lyrics, hard to be in a bad mood listening to fifties and sixties motown
It depends on my mood. Some times I can sit there and pound away at the keys with just the TV droning away in the background. Other times I listen to whatever is the latest set of songs I have discovered. Then there are the times I just type away in silence.
I use songs in my stories, but not because they are running at the time I'm writing. And songs only rarely prompt story ideas for me. I usually have the story idea and reach back to incorporate something from a song I know--more often than not, a classical song or an older pop tune.