This post originally started as a comment on Falstaff's blog. And precisely when I hit the submit button (after duly entering in an inordinately long word for the sake of verification) blogger chose to go down, and this was left unsaid.
While I agree that the Rolling Stones was one of the greatest rock bands ever, I am a bit leery of nostalgic characterizations of all bands from that generation as revolutionary. As a rock and roll band, the Stones were pretty mainstream, and my belief is that bands like the Stones had it easy by piggybacking along the backs of a social movement that started during the euphoric years when the post war generation grew up. As a band, I do not think their music was all that inspirational.
The history of rock and roll (and of music in general) has been of breakaway movements that got assimilated into the mainstream, and typically bands that chose to so sell out are the ones that saw commercial success and are remembered with nostalgia. Those that 'stayed true' (such as VU in the '60s, or Sonic Youth from the '80s onwards) remain quite obscure, apart from a small core of fans that truly appreciate what they were worth. It was these bands that had the greatest degree of influence of what was to come. The Velvet Underground was the inspiration for the punk and new wave movements in the seventies and early eighties. Sonic Youth has influenced almost every genre of alternative rock (which, arguably, has become quite 'mainstream') over the last twenty years, while still remaining relatively obscure. Or we could take the example of the Pixies, who were the precursors of grunge and heavily inspired bands like Nirvana, Pearl Jam and the likes. It is the latter that have had a lot of commercial success and will be remembered as symbolizing that genre of music years from now.
The closest analogy to the Stones that comes to my mind is that of Nirvana, which having been heavily influenced by the alternative scene of the time, went on to become one of the most popular rock bands of our times. Nirvana will be remembered with nostalgia, but they will never have the kind of influence that bands like SY and the Pixies will have on subsequent cultural movements in music.