Best American Band

[Donnyho]

I think you could make a pretty strong case for it being R.E.M..  They had longevity (formed in 1980, broke up in 2011), one line up (when drummer Bill Berry left for medical reasons in 1997 they became a trio and never replaced him), they've sold 85 million records worldwide, and are in the Rock and Roll Hall of Fame.  They're also influential musically (Kurt Cobain being extremely vocal about it) and critically acclaimed.  

So you've got a band that started on and indie, were very successful, signed to a major label, became even more successful, influenced a generation of artists, never sold out artistically and made critically and commercially music through their entire career.  Sounds pretty good.