As for staying power as group, got to hand it over to the Rolling Stones. From the mid 60s "second string" to the Beatles, through the 70s "greatest rock'n'roll band" till the 2000s "grandfathers of rock".
The Rolling Stones album Sticky Fingers seldom appear on any favorite list, but I think it's one of the best. Many people quote Brown Sugar but few quote its motherboard album Sticky Fingers (try amazon.com etc., because I think it's still banned in Singapore.) The other great Rolling Stones albums are of course Beggars Banquet and Let It Bleed, very frequently quoted by critiques as rock essentials.