I could not begin to choose.
If you go by the number of CD's I own of a certain group it would be:
The Beatles, REM, U2, and The Eagles/Don Henley.
You almost have to break it down into categories:
Classic: Beatles, Stones
Theatrical: The Who, Queen
Reflective: Zeppelin, Floyd
Blues: SRV, Clapton, Bonnie Raitt
College years: REM, U2, The Police
Grunge: Nirvana, Pearl Jam
Country/southern Rock: Eagles, CCR, Skynyrd, Garth Brooks
Just plain great: Fleetwood Mac, Bruce Springsteen, Simon and Garfunkel, Jim Croce, Melissa Etheridge
Soul: Aretha, Marvin Gaye
Motown: well, Motown, all of it.