I don't have a definite taste for a particular genre of music, mostly what's currently popular.
I also tried to learn the violin for a while at some point, so I do listen to classical every now and then.
Tho, specific for songs, I value lyrics over anything else.
I care about the complexity and creativity of the story being told, the rhyme of the poem, things like that.
I don't really care about the genre or the artist, but if I simply find the lyrics too lazy (or I simply can't understand what the singer is singing), I'm not gonna like it.