I'm more specific about what kind of music I listen to when I run than when I am lifting weights. I find that if I listen to music with a heavy and fast beat when I'm running it makes me go too fast and tire too quickly so I like to listen to ambient music or ethereal dream pop type stuff.
ie Ulrich Schnauss, Cocteau Twins, Slowdive, Chameleons UK, Lush, etc.