Actually, I like the BEST of so many different kinds of music that it's easier to say what kinds I DON'T like. My least favourite, probably because I don't even classify it as "music", is rap. To me, if you can't whistle it, it doesn't qualify as music because music without a melody is just noise. Rap is just ranting, with an irrelevant loop playing in the background.
Heavy metal, with people screaming at the top of their lungs, is hard on the ears. I like "smooth jazz", the relaxing, easy-listening kind. I probably listen to it most on the radio -- but I HATE free-form jazz where everyone plays any old note apparently at random, except the ones in the tune. I love some of the country "hurtin' songs" that sound like folk poetry, straight from the heart.
And I've been to Istanbul three times in three years, and love MOST Turkish pop music I've heard, because it's so interesting to listen to, with melodies that do neat and unexpected things. It makes so much pop music that's in English sound really bland. I've got nearly 50 CDs of it, now.