I think it would be more accurate for me to list what I don't like rather than what I do--because I like many different styles of music. Even so, I find that I mostly enjoy and mostly buy that of the greater rock type. And to be honest, some of my favorite bands produce......crap. But I don't care.
What I don't like is brassy jazz, and the contemporary pop types, disco, some others. However, even within the categories of music I don't like, I can usually find a song or an artist whose music I enjoy. I discover them most often by recommendation from someone.
Thing is, even those styles I don't normally like, I can enjoy when in the right context. Live performances tend to facilitate that more easily than recordings.
Recent discoveries, and bands/artists that I am currently listening to nearly everyday since are the Black Keys, The National, John Grant, Imogene Heap, Live, Dan Sartain.
Old favorites include k.d.lang, Texas Tornadoes, Zepplin, Leonard Cohen, Nick Lowe, Poets of the Fall, Rammstein (helps me with my German), Staind, Them Crooked Vultures, Audioslave,.......I could go on.