Classical (fav. inst. piano, violin, specially concertos with them as main inst)
Heavy/thrash/speed/power/death/alt metal
Classic/alt/J/ballad/pop/folk rock, rock & roll
Some pop, like J, adult contemporary (like Celine Dion), eurobeat, classical crossover (Il Divo, as an example that most will know).
Aside from all that, I can really listen to anything that is at least a bit complex in nature, beyond commercial three/four notes tunes with cheap writing, which I don't entirely dislike, I just wouldn't listen to it to entertain myself. Same goes with things like Spanish folk, the only kind of Spanish folk I like is Spanish folk-rock and a few Spanish metal bands. Always preferred songs in English and poems/novels in Spanish, myself.
When it comes to rap/hip-hop and similar, same goes. I'm not a big hater but don't expect me to listen to it since, well, I don't like the style and that's it, as good as it may be. There's only a few songs I'd listen to, and those aren't pure rap or hip-hop, rather mixed with other genres.