The Doors, The Velvets, REM, Nirvana, in that order I think. It's hard to find a more influential band that the Velvets, but they only had a couple of albums and they only gained recognition after they'd split up, really. The Doors were a legit stadium band and were also massively influential. Nirvana obviously don't have the back catalog to really carry weight here but what they did has echoed loud and long, probably more so than REM, although a Greatest Hits of REM would be far more fun than a Greatest Hits from Nirvana.