Generally I can listen to anything, minus MAINSTREAM rap, and screamo. Shit's terrible. Underground rap/hip-hop however, can be pretty good stuff. Country/Southern is good if you look in the right places (Outlaws, Charlie Daniels Band, Lynyrd Skynyrd etc.)
I enjoy some alternative, reggae, folk, death metal, pop, jazz fusion, experimental rock, techno, classical, prog, hair metal, and the list goes on.
Mostly I'll listen by band rather by genre though. For example, you've got shitty power metal like Dragonforce, and then you've got great power metal like Sonata Arctica or Stratovarius. Same formula, pulled off by different bands, with each adding in their unique flair.