I'm more a writer than a musician so get writing ideas and "stories" when I sleep. My music dreams are usually me getting instruments mixed up (thinking an instrument is one thing and calling it that and waking and knowing it was another :-) though I did have a couple nights when I woke with a specific song in my head that would not go away but, alas, it was a known piece of music not something new.

Very interesting study on music in dreams: http://web.mit.edu/dmalt/Public/9.10/02sdarticle.pdf