Unfortunately I don't have many CDs. I don't usually buy them.
And my computer sucks so much that I can't download music from the internet very easily...
So typically I listen to video game music.
My favorite games for music:
Final Fantasy series (each one has at least 2 or 3 tracks that are among my favorites)
Castlevania: Symphony of the Night (great techno-classical type stuff... somehow electric guitars blaring alongside pipe organs doesn't seem weird...)
Sonic games (my love of video game music first started after hearing the themes from Green Hill Zone (#1) and Ice Cap Zone (#3, not #3&k))
MegaMan music (this rocks! it's just so great - especially the X series)
Donkey Kong Country (on SNES, especially #1, but some of the tracks in #2 and #3; the music in #1 is so atmospheric - you rarely get music like that in games today. I like some of the music in the other DKC games as well, but not as much as #1)
various other games I've played, most of them Japanese games; typically the classic games (Mario, Street Fighter, Zelda, etc.) and some more recent ones (Tekken, Crash Bandicoot, etc.)
(So when a game has very little music, I get pissed.)
I wish they would package soundtracks of games with them, like they do in Japan!
I also like anime music.
And if I hear some J-Pop, I suspect I'll like that, because most of the music I like sounds so distinctly japanese (not traditional japanese... you know what I mean) that I'm guessing it's sort of like that, but not as techno.
Mostly the only time I listen to music is when I'll walk around humming tunes that no one else will have heard of. Fortunately I'm equipped with a fabulous auditory memory, so I can go recall a random tune and sing it perfectly, and remember the exact context in which I heard it 2-3 years ago.
I do listen to other kinds of music; in general I prefer classic (specifically progressive) rock (late 60s, early-mid 70s mostly). Other than that, I'll probably listen to just about anything... I despise country, but I can sit through bluegrass and wait until the end of the song to puke. I typically don't like boy/girl bands; only occasionally can I stand some of their songs, and usually because those songs borrow from some other type of music which I like, and in that case I can just listen to that music anwyay.
EDIT: PROG PROG!
Yes (lots and lots of Yes, 70s and 80s)
King Crimson
Primus
Pink Floyd
Sigur Rós -- their new album ( ) is great!
Mahavishnu Orchestra esp. Birds of Fire
Emerson, Lake, and Palmer
Jethro Tull Pretty good
Gentle Giant
Beatles
Godspeed you black emperor