All Radiohead
-ALL- Boards of Canada (Especially their remixes)
All Múm
All Portishead (Especially Live at Roseland)
All Lush
All Cocteau Twins
All. ALL Hope Sandoval (Incl. Mazzy Star)
All Radiohead (excl. Thom Yorke's solo work)
All Regina Spektor
Air - Talkie Walkie & Moon Safari
Annie Lennox - Medusa & Diva + Eurythmics
Aminamina - Self-titled
Autour de Lucie - Self-titled (there are two of them), Faux Movement & Immobile
Biosphere - Substrata
Bjork - Debut & Post
Broadcast - The Noise Made By People, HaHa Sound, Tender Buttons, The Future Crayon
Blur - Best Of (sorry, they're a hit machine)
Boom Bip - Corymb, Circle
Camera Obscura - Let's Get Out of this Country
Camille - Les Sac Des Filles, Le Fil
Chemical Bros. - Dig Your Own Hole, Exit Planet Dust
CocoRosie - Le Maison de Mon Reve, Noah's Ark
Cyann & Ben - Happy Like An Autumn Tree, Spring
DJ Shadow - Preemptive Strike
Elliott Smith - XO
Emilie Simon - Vegetal
Fennesz - Venice, Field Recordings
Fiery Furnaces - Bitter Tea, Blueberry Boat
Fiona Apple - Tidal, When The Pawn...
Goldfrapp - Felt Mountain (WHY ALLISON?!)
Hooverphonic - A New Stereophonic Sound Spectacular
Johann Johannsson - IBM 1401, A User's Manual
Kings of Convenience - Self-titled, Quiet Is The New Loud
Koop - Sons of Koop, Waltz for Koop
Le Volume Courbe - I Killed My Best Friend
Ladytron - Witching Hour
M83 - ...eh...All.
Malajube - Trompe l'oeil
Mira Calix - Nunu, One on One
Morcheeba - Who Can You Trust?
Prefuse 73 - One Word Extinguisher, Vocal Studies + Uprock Narratives
PJ Harvey - Is This Desire, Stories from the City, Stories from the Sea
Prodigy - Fat of the Land, Music For The Jilted Generation
RJD2 - Deadringer (Try like hell to find his remixes, too)
Royksopp - Melody A.M.
Sleater-Kinney - The Hot Rock
Slowdive - Souvlaki, Pygmalion
Sneaker Pimps - Splinter, Becoming X
St. Vincent - Marry Me
Stars of the Lid - The Ballasted Orchestra
Stereolab - Margerine Eclipse, Emperor Tomato Ketchup, Oscillons from the Anti-Sun
The Bird and The Bee - Self-titled
The Flaming Lips - Yoshimi Battles the Pink Robots, The Soft Bulletin
The Fugees - The Score
The Innocence Mission - Befriended
The Libertines - Up The Bracket
Thievery Corporation - The Mirror Conspiracy, The Richest Man in Babylon, Sounds from the Verve Hi-fi
Tricky - Maxinquaye
Zero 7 - When It Falls, The Garden, Simple Things
I tried to omit too many obvious selections, but definitely check out Sting, Sade, and the like. If you aren't already listening to Coltrane or The Beatles or Dylan, etc., then take go out back and do something bad to yourself.