Well, I tend to listen to music you would hear a snippet of from a random commercial that, if you either look it up online and/or read that "one" magazine that points out music in commercials, you would find out that it's an actual song that you can listen to on an album from some indie band/group that has been making music longer than you would first think upon further "google-searching"...
Other than that, I can put every song I listen to, in general, into "several" categories:
-Adult Swim music (as in music used in those Adult Swim bumps/commercials/shows)
-Anime (besides Openings and Endings of various anime series)
-Classical (especially if there's a piano of some kind involved in the musical piece itself)
-Gorillaz (We seem to think alike, OP...)
-Hip-Hop (NEVER confuse this with Rap in general... Call it a "pet peeve" of mine...)
-Mashups (Either be popular/mainstream songs mashed together... or rap songs mashed up with anime songs... Whichever's the case...)
-Musicals/Showtunes (Listen to those WAY before watching Glee... but, "ironically", not before watching Fame for the first time...)
-Nerdcore (Rapping/singing about video games and nerd culture...)
-Nujabes (This dude's has his own category... R.I.P, man...)
-Ponies (Ponies ponies ponies SWAG!)
-Rap (pre-50 Cent, with a few exceptions listed under other categories...)
-Video Game OSTs (Always self-explanatory...)
-20th Century music (Too many genres to list, but they all seem to fall under that "turn of a century"... How about that?)
-Electronic (Honorable mention, but still...)
Then again, I can basically listen to anything and not [fully] complain about it... Just not care as much as some of the other music I normally listen to, anyway...