Prog Rock (Pink Floyd, Tool, Cog)
Prog Metal (Dream Theater, Symphony X, Opeth)
Classical (Bach, Paganini)
Neo-Classical Shred (Joe Stump)
Classic Rock (Led Zeppelin, Lynyrd Skynyrd)

I also like songs/bands that are in genres that I don't particularly listen to or like, such as:

Ambient DnB (Aphex Twin)
Hip-Hop, not rapping but mixing records (Katalyst [the only known artist to have a good remix album], Dynamo Productions)
Psychedelic Rock (some Oasis, Radiohead [before the mindless wailing and moaning], Gelbison, Deloris)
Speed Metal (Slayer)
Bluegrass (Hellecasters)
Grindcore (Pig Destroyer, Blood Duster [perhaps better described as porngroove metal])
Punk Rock (The one song by Frenzal Rhomb, 'Russel Crowe's Band'. A very funny, short song. It even has a solo although it's just a simple pentatonic one.)