Sonic Youth
Flaming Lips
Animal Collective
Tom Waits
Jackie-O Motherfucker
Spiritualized
The Cure
GY!BE/A Silver Mt. Zion
Madlib
Fugazi
Jesus and Mary Chain
Velvet Underground

That's all I got.

Sonic Youth
Rage Against the Machine
X
Pixies
Santana (in all forms)
Hendrix
Allman Bros.
Neil Young
Doors
Rashan Roland Kirk
The Stones
Pink Floyd
J Giels
Clash
Diana Ross (with and without the Supremes)
Four Tops
Johny Cash
Bob Marley
Charlie Parker
Marvin Gaye

Surprised I haven't done this....

Top 10:
1)Pavement
2)Dinosaur Jr
3)Modest Mouse
4)Polvo
5)Built To Spill
6)The Pixies
7)Guided By Voices
8)The Cure
9)Swervedriver
10)Superchunk

Next ten in no specific order:
Sebadoh
Mission of Burma
Sonic Youth
Galaxie 500
Jawbreaker
Swirlies
Unwound
Pearl Jam
Spoon
Beat Happening

Something like that....

~Jeremy~

Sonic Youth
Nirvana
Pantera
Pink Floyd
Radiohead
Massive Attack
Black Rebel Motorcycle Club
The Vines...yes, that's right, the Vines. I think they're the most underrated band of the past 10 years. Get over it.
Fugazi
Minus the Bear
TV on the Radio
Messhugah
Ministry
Smashing Pumpkins
Porcupine Tree
Miles Davis
Ludwig van Beethoven
The Smiths
Metallica...only because they were one of the first bands I ever really got into. They've done a lot of crap (both on and off record), but they'll always have a place in my heart/record collection.

Random order, limited to 20th century:

John Coltrane
Charles Mingus
Olivier Messiaen
Luciano Berio
Béla Bartók
Alfred Schnittke
Tim Buckley
Slint
Charalambides
Claude Debussy
Sonic Youth
Morton Feldman
Per Nørgård
Steve Reich
Velvet Underground
Nels Cline
K.R.T. Wasitodiningrat
Giacinto Scelsi
David S. Ware
Ornette Coleman