Oh Boy, This could be a DOOZY of an answer provided I can think clearly about it!:
U2 - October, Drowning Man, EP&America, Bad, AIWIY, LRM, One, So Cruel, LIB, Please, IGWSHA, Stay, SIAM, Kite
Tori Amos - Winter, Silent all these Years, Tear In Your Hand, Caught a Lite Sneeze, 1000 Oceans, Northern Lad, Little Earthquakes
Fiona Apple - Never Is A Promise, ShadowBoxer, Carrion, I Know
Blur - Tender, No Place Left to Run, This is a Low
David Bowie - Space Oddity, Under Pressure
Leonard Cohen - Suzanne, Sisters of Mercy, That's no Way to Say Goodbye, Famous Blue Raincoat
Coldplay - Yellow, Trouble
Cure - Letter to Elise, Cut, Pictures of You, Trust, Apart, High
Depeche Mode - Question of Lust, Breathe, Only When I Lose Myself
PJ Harvey - To Bring You My Love, Send His Love To Me, You Said Something, This Mess We're In, Angeline
Billy Joel - Honesty, Piano Man
Mazzy Star - Fade Into You, Halah
Radiohead - Exit Music, Karma Police, Fake Plastic Trees, High and Dry, Pyramid Song, Paranoid Android
Random:
10cc - I'm Not in Love
This Mortal Coil - Song to the Siren
Howard Jones - No One is to Blame
Enya - Only Time
Toto - Africa
GNR - Patience
Natalie Imbruglia - Identify