LS has many great songs Tuesday's Gone, Simple Man, Gimmie Three Steps, Saturday Night Special, That Smell, Gimmie back my bullets, Call Me The Breeze, What's Your Name, etc.
I would say they are one of the best American rock groups of all time.
There are so many good ones:
Slayer
Allman Brothers
Doobie Brothers pre-74
CCR
Boston
Buffalo Springfield(yea I know not all members are American)
Elvis(though not really band)
Johnny Cash(once again not really band wise)
The Ramones
The Melvins
The Eagles
MC5
Iggy and the Stooges
Van Halen
Black Crowes
Blue Oyster Cult
Faith No More
Metallica's first four albums
Janes Addiction
Tom Petty
the doors
The Boss
Pearl Jam
Hank Williams
Robert Johnson
BB King
Bo Diddley
Bob Dylan