Saint Vitus damn well could have been had those guys not been born too late
Pat always did have his head on straight. 
I’m pretty sure most casual listeners would know “Ramblin’ Man.”
Probably I’d say Orleans.
(“Dance With Me”)
Dude, if you’re gonna offer Orleans, state their best song: You’re Still The One. 
If you ignore the fact that “American” really means “United Statesian”, the answer is clearly Rush, who are clearly from a place that is part of America. I’m probably biased toward them since I’m a pretty big fan though.
I think I would go with Van Halen personally. I don’t really like them that all that much, but any history of rock music discussion is going to include them if only for “Eruption” as well as the wave of similar bands they started. They were extremely popular with several number 1 albums and managed to survive a change in lead singers. The only ones that I think come close in terms of popularity and longevity are Aerosmith, and they’re not as notable historically. Everyone else mentioned isn’t really a band or really isn’t all that widely popular.
Since you just put that in my head, let me return the favor with this “cover” of that tune. That must have been an impressionable year for me, as I still get that stuck on a loop from time to time.
As an American who spends a lot of time in Canada, I’ve never encountered anyone who felt this way. The distinction between “American” and “Canadian” is readily understood, and “American” is almost universally recognized as shorthand for “from the United States of America.” I’ve never, ever heard a Canadian say, “we’re part of North America, so we’re technically American too.” If anything, they’re proud NOT to be associated with the US.
I love Paranoid, but I do not think of it as some kind of proto-punk rock. If anything, I’d say it was reminiscent of Zeppelin.
I’m not a huge fan of the Ramones or of punk rock generally, but I can understand the idiom and understand the importance of the Ramones. The Ramones introduced punk rock concepts that Black Sabbath did not use:
Simplicity
Repetition
Playfulness
If anything, they were drawing from pop traditions, not hard rock ones.
Aahhgg!! Don’t do that! 
Especially these days, yes.
Sabbath is awesome, but I’d say they’re the godfathers of heavy metal. Ramones are the progenitors (or one of the progenitors) of punk. Two different genres (although they did eventually cross pollinate).
Like some other perennial Doper favourites (Rush, for one), any judgement on “continuing influence” is going to have to take into account the fact that the Dead are not all that well known in some other parts of the world. I mean, I know who they are, but I’ve only, ever heard them incidentally. I could not pick out a song of theirs, and I’ve never seen a video of them. They did not get much airplay in South Africa, not even on oldies and blues shows. I could probably sit down and name 50 more influential rock acts here without really thinking.
My answer to the OP would be the Beach Boys. I mean, Pet Sounds alone…
Again, nearly completely unknown in South Africa.
No, they’re really, really not. I know, as trivia, that punk “started” in NY, and that the Ramones are “punk”, but the scene here starts with the UK in '76 and only really notices the US when Hardcore kicks in. Here, the Ramones are a footnote, not a touchstone.
Lots of people wearing Ramones t-shirts, though - but less than the number wearing Misfits shirts, and orders of magnitude more than could name a Ramones song. Because the answer to
is “yes”
Tell that to John Lydon:
“No New York Dolls, no Sex Pistols”, I could understand. But the Ramones? Naaah.
What I’ve been saying all along. Apparently I know two Grateful Dead songs and one Ramones’ song.
Not really internationally influencial!
The Beach Boys win this title by a landslide.
Like I said, I know 0 Dead songs. I do know “I Wanna Be Sedated”, but that’s from recent VH1 plays, not from my days as a punk kid.
However, I’m all about the Velvet Underground and the Stooges.
The funny thing, for me, is the OP started talking about the Beatles as a given for GOAT, but “no Pet Sounds, no Sgt. Pepper’s Lonely Hearts Club Band” is easy to show. Unlike, say, the Ramones’ supposed influence on the Pistols
Aren’t you glad you don’t have an editor yelling at you “Hey, where’s that article ‘Greatest American rock band ever’?" You’ve had a whole day, and we go to press in an hour. Who’d you pick?”
Random reactions to random comments:
If anyone doesn’t have the Joni Mitchell albums with that band (Shadows & Light and the live Miles of Aisles), it’s an amazing live band…
Tasty Guitar; Pat Metheny
Keyboards; Lyle Mays
Amazing Bass; Jaco Pastorius
Drums; Dom Alias
90s Sax; Michael Brecker
Guitar (mostly electric); Joni Mitchell
DooWop Vocals; The Persuasions
I totally agree on Jerry’s ‘ordinariness’. A bandmate who knew his shit once made the comment that Jerry Garcia and Jackson Browne had no vibrato.
If (like me) you’re not wild about Jerry’s vocals, don’t forget all the great Bob Weir tunes that Jerry mostly just played guitar on. Seriously, do listen to *“Cassidy” *-- moody masterpiece (nice guitar licks, evocative lyrics --Robert Hunter?-- and great vocals… with vibrato!).
Here’s the Dead version, but it’s on Weir’s beautiful “Ace” album.
And a recent acoustic trio:
And another Bob Weir tune, just to prove he can sing:
