As I have said elsewhere,I think the music should change with each passing era in history;e.g.during the middle ages the music should be representative of what was popular at that time in history.I think this is the best way to immerse yourself in the game and make you feel more like you are actually there.
Everything. I agree with DanM, the music changes with the era.
Maybe a simple change between types of civs aswell for selected parts of history:
European music, African music, Asian music, Native American music.
How about the music changes a few years after an advance, like after electronics you get a bit of heavy metal or electronic?