It's like potato chips. You can't have just one!
I was brought up on classic rock, so I still like me some classic rock. Oldschool East coast punk, black metal, Jpop, triphop, Goth, these are all types of music I listen to on a regular basis. Any kind of world music. If I haven't heard it before I'm going to be curious about it, so whenever I am browsing the grooveshark broadcasts and I see some title in a language I don't speak, I might toss that song in my playlist just to hear how this band sounds.
There are a lot of types of music I don;t like in general, but there will be a few songs, or a few bands in each genre I like anyway. For example? Not a big rap fan. And yet there are rap songs I like. Ditto country. For the most part I rarely get an urge to listen to a block of country music, but the country songs I do like I like quite a bit.
My 'rents brought me up trying to make sure I had a wee bit of class, so I listen to jazz and orchestral ('classical' music; although the term 'classical' actually only refers to a specific time period of symphonic music) occasionally. About the oddest thing I am fond of is novelty records, the kitschier the better. My music tastes are all over the board, but you could always ref my
last.fm if you want a more specific idea.