There's very rarely a genre which I categorically don't like. Rap/Hip-hop is one of those.
In every other genre, I tend to only listen to the examples which are doing interesting things harmonically, rhythmically, or demonstrate real, exceptional talent. This means that on any given day, I can go between Ambient/Electronic, Post-Rock, Classic Rock, Metal, Jazz, Classical (all periods/styles), Pop, and so on.
My personal favorites are
Classical (As you might guess, I'm a clarinet player, and focused on the 20/21st century styles in school. Stravinsky and Mahler are personal favorites),
Jazz (not 'smooth jazz'),
Post-Rock (Godspeed You! Black Emperor, God is an Astronaut),
Other Experimental styles (Capillary Action, Battles, Mr. Bungle, 65daysofstatic, Don Caballero, Hella, and The Mars Volta), and
Classic Rock (The Beatles and Pink Floyd especially)