Related to the Favorite Song of All Time thread, here's a (mostly complete) list of about 100 of my favorite bands/composers. It was too daunting a task to put them in order of how I like them, so I just put my (current, ever-changing) top 10 roughly in order (top 3 are definately right), and the rest are in alphabetical order.

Jimi Hendrix
Emilíana Torrini
Björk
Elliot Goldenthal
Evanescence
Cake
Alice in Chains
Muse
Apocalyptica
Simon & Garfunkel

Alice in Chains
Anúna
Apocalyptica
The Beatles
Billie Holliday
Björk
Black Box Recorder
Blind Melon
Blink 182
Bob Marley
Cake
The Canadian Brass
Carl Orff
The Carpenters
The Chieftains
Christopher O’Reily
Clannad
Coldplay
The Cranberries
Danny Elfman
David Arnold
Dead Can Dance
Depeche Mode
Dizzy Gillespie
Doc Severinsen
Duke Ellington
DVDA
The Eagles
Elliot Goldenthal
Emilíana Torrini
Ennio Morricone
Enya
Eurythmics
Evanescence
Flogging Molly
Green Day
The Guess Who
GusGus
Gustav Holst
Hans Zimmer
Harry Connick, Jr.
Herb Albert and the Tijuana Brass
Hoobastank
Howard Shore
Incubus
J. G. Thirlwell
Jack Johnson
James Horner
James Newton Howard
Janis Joplin
Jefferson Airplane
Jethro Tull
Jimi Hendrix
John Williams
Joni Mitchell
Katie McMahon
Lacuna Coil
Ladysmith Black Mambazo
Led Zeppelin
Lila Downs
Linkin Park
Lisa Gerrard
Loreena McKennitt
Louis Armstrong
Maire Brennan
Massive Attack
Méav
Metallica
Muse
Nina Hagen
Nirvana
Nobuo Uematsu
Nora Jones
P.D.Q. Bach
Paul Oakenfold
Paul Simon
Peter, Paul and Mary
Philip Glass
Portishead
Queen
Queensryche
Radiohead
Rammstein
Red Hot Chili Peppers
Sarah Brightman
Sigur Rós
Simon & Garfunkel
The Smashing Pumpkins
Sneaker Pimps
Stephen Lynch
Steppenwolf
The Swingle Singers
System of a Down
They Might Be Giants
Tom Jones
Tom Lehrer
Tori Amos
Tricky
Various Artists (Just Kidding)
“Weird” Al Yankovic
The Who
Wynton Marsalis