I think all the posts advocating for people to absolutely not listen to any music here are interesting. For me, music is an integral part of my life, and to remove the pleasure I get from listening to music while riding is tantamount to taking away the riding itself! I find that even with two headphones, it's very easy to remain safe so long as you yourself are on alert at all times. Be smart about you and your limitations and you shouldn't be any less safe listening to music than without it.
As for what I liste to specifically, I really couldn't list every genre I enjoy, because I enjoy a lot. I will say that I tend to lean towards more dynamic, instrumental music while riding as opposed to something softer and ethereal, or something lyrically dense that requires absolute focus. Like, I really old school east coast hip hop, and instrumental remixes from that era, as well as electronica and vaoprwave.