In resonse to a few notable objections, and to explain my thought process:
The Clash/Ramones
Iggy Pop and MC5 essentially created punk, and so I believe them to be the most influential. All are born of Iggy's denim clad loins.
Hendrix, Elvis, etc.
People aren't really a "band" per se. Danzig was associated with bands when his influence was truly made evident, thats why he is an exception.
Metalicca
Were born of Motorhead, as was most metal that became popular in the 80's and 90's, if you ask them. They took the place of Black Sabbath in influence, if not talent.
Black Sabbath
See above.
Nirvana
They are my truly noteable exception, but I wouldn't put them on this list, because I believe they are a collection of influences more than anything. Also, listening to music that came out after them, they didn't influence music all that much. Or maybe thats just wishful thinking considering all the absolute SHIT that has come out as Rock and Roll post 1995. They influenced a generation, but I don't think they had enough time to infleunce music (and NO, they did NOT create grunge). Also, putting Nirvana on the list would open a whole can of worms including Faith No More and the Melvins, as KG said.
The Foo Fighters
You gotta be fucking kidding me...
Black Flag, Velvet Underground and Pink Floyd are all great picks, IMO. I really struggled with not having Pink on the list. Looking back on the lst, I think it suffers from trying to have too many influences on it, rather than just the MOST influential.
And people, lets not just post the names, LETS GET SOME YouTube vids up in this piece!!!