I'll listen to anything but really dumb rap and death metal/screamo. I really like alternative rock, 80s rock (not bands like Aerosmith or KISS, though, ugh), progressive metal, and indie.
My favorite bands include Coheed & Cambria, Pain Of Salvation, The Police, Oingo Boingo, Cake, Dead Celebrity Status, Tub Ring, Flobots, and The Decemberists.