No particular order, but I love each of these groups in one way or another:
Blur
Gorillaz
Graham Coxon
The Good, The Bad And The Queen
Super Furry Animals
The Specials
Ladytron
Cathy Davey
Beck
Cornelius
Pavement
Stephen Malkmus
Jon Spencer Blues Explosion
Beastie Boys
Money Mark
Eels
Beth Orton
Joy Zipper
Stereolab
Denim
Electralane
Air
Saint Etienne
Birdie
Pizzicato Five
Supercar
Plus-Tech Squeeze Box
Guitar Vader
And to those I've forgotten, I apologise...