Who do you think is the GREATEST AMERICAN BAND of all time?
It really depends on when you grew up.
Currently my favorite is Tom Petty and the Heartbreakers. They are one of those bands that you don't really know how great they are until you see them perform live. They are better live than on recording and you find yourself singing every song they perform. For the new generation, the "Foo Fighters" are really comparable to the Heartbreakers.
There were some great bands like Aerosmith and Guns N' Roses who couldn't get out of their own way and restricted their own development with various issues.
Bon Jovi and The Eagles had their runs of domination.