Or complimentary pairs that fit together like a jigsaw puzzle. The bands don't necessarily have to have hated the living shit out of each another.

The Beatles / The Rolling Stones
Pink Floyd / Yes
David Bowie / Roxy Music
The Clash / Sex Pistols
Joy Division / Buzzcocks
U2 / Echo & the Bunnymen
The Smiths / The Cure
The Stone Roses / Happy Mondays
Guns N' Roses / Nirvana
Oasis / Blur
Pulp / Suede
Radiohead / Manic Street Preachers
Smashing Pumpkins / Placebo

What else is there?