Oh man, I listen to an incredible amount and variety of music. It would probably be easier to list off what music I don't like. Generally (there are a few exceptions), I do not like music belonging to the genres of: hardcore punk, death/doom/crap metal, emo, screamo, scene, contemporary pop, 90's pop, country music from the time of and after Billy Ray Cyrus, mainstream rap, mainstream hip-hop, opera, classical (though there's some great neo-classical out there), and KISS (Gene Simmons particularly). If it was made recently, I probably won't like it, because modern music has a tendency to suck. And if it has a tendency to suck, then I probably won't like it.
Let me emphasize again that the music listed above is stuff I do NOT like. Below is some stuff I DO like.
These genres in particular are held very near and dear to me: grunge, 80's pop, 80's metal, gangsta rap, and 70's prog.