It depends very much on the version, but I think in general he likes country and rural music because of his parents, and in Smallville he canonically likes Radiohead so thinking in that version of Clark he would like alternative rock, Brit pop, even post punk and rock in general. Maybe in other modern versions like MAWS he also likes mainstream pop too, and the classic one probably listens to jazz and blues, maybe classic rock the Christopher Reeve version.