Which band IS really America's Greatest (rock & roll band)?

Such a tough call. If one were to factor in the impact of the band on the rock n' roll scene (in other words the context in which the band emerged and their impact on the course of rock history) then I would have to put R.E.M. near the top of the list. By the early 80s rock was a decadent, dying, caricature. R.E.M. brought rock back to it's roots with a vitality and energy that was sorely needed. I remember blasting Murmur in my car on the way home from college and thinking "thank god for this band". In 1983 rock needed and revival and I think it can be argued that R.E.M. led the way. Also, being from Jersey, I'd have to put Springsteen up there as well. He took rock storytelling to a whole other level. As I write I think my choices are interesting in that Bruce was as much about the words as the music and you couldn't understand a word Michael Stipe was singing until the release of "Green". 

For their influence the Velvet Underground.
For music pleasure CCR and the Allman Brothers.

Agree with you dodgealum. R.E.M. sounded so different. In addition to starting out 'indie' and different, they were able to catch the MTV wave and ride right up into stadiums and super group status.

I think when considering 'greatest' discussions that popularity, sales and charts are important. I don't think they should be THE criteria but I still think you have to take it into account. There are a lot of artists listed here that are great in their own right but relatively obscure, or short lived that no matter how good they were really don't rise to 'greatest of all times' status. Certainly influence is important but I think in terms of 'greatest' all of these things have to be there.

Sly and The Family Stone...

The "most American" band would have to be "Indigenous", three siblings and a cousin from the Nakota Nation, So. Dakota.  Listen to "Things We Do", their first album, 1998.  Blues guitar phenom in the style of SRV.