He’s not a band. And he is well known for demanding that promoters provide him with a backing band, who he would usually meet for the first time when he walked on stage to begin his set.
I think that Sparks deserve at least an honorable mention here. That’s 40 years with only a name change and the backing band.
Guinness, like Wikipedia, can be used as a starting point, but since they only list things that have been reported to them under their specific conditions, they list things that nobody would have thought of reporting if it wasn’t for Guinness (“person to eat most hamburguers in one sitting”) and they don’t verify whether something reported to them is actually the mostest (the person I saw listed as the youngest king was 14; Fernando XIII of Spain has him beat at minus four months and this isn’t exactly obscure knowledge).
I’ve been thinking of Spanish groups but can’t come up with any that have been working continuously with the same lineup and which do rock. Golden Apple Quartet have been together 17 years, but they’re vocal; Mocedades have been together since 1969 and their last record to date is from 2007 but they’re a mixture of folk and pop and there have been lineup changes (although it’s still basically a case of “Uranga siblings and spouses”). Revólver have been together since 1988 but there have been lineup changes, as have been in Loquillo y los Trogloditas (since 1983) or Rebeldes (since 1983 as well). There are quite a few groups that have been together 30 years or more but which are rock only if you include “flamenco rock”, a brand which I imagine would be hard to find outside of Spain 
All original members seems way too narrow. You could count those bands on one hand. If you loosen it up to bands with a majority of original members, there’s quite a few more.
Judas Priest has always had KK Downing, Glen Tipton and Ian Hill since 1974, with Rob Halford most of the time, a Spinal Tap-esque parade of drummers, and a seven year hiatus.
The Rolling Stones have had Richards-Jagger-Watts since 1962.
If you ditch all original members, Jethro Tull is way up there.
Why even a majority? Why make personnel the criterion anyway? Wouldn’t the most telling have something to do with, like, continuity of artistic vision? (Which is not to say an unchanging artistic vision, just an unbroken, ongoing one.)
I rather suspect that if it’s original members, their artistic vision may be beginning to wane as they approach their sixties and seventies, and if it’s not original members, they’re probably piggybacking on the original members’ vision.
How would you define continuity of artistic vision?
Anyway, this thread was just a trivia question asking about the longest lasting rock band whose line-up hadn’t changed.
I’m finding myself reminded of when Will Smith’s cousin Carlton was on a quiz show.
The Chicago Tribune has a long article on this question today using virtually the same parameters, on the occasion of an album of new material from The Ides of March, formed in 1964. All four original members are still with the band, best known for the hit song “Vehicle” in 1970 (went to #2). They may not count for this thread, though, due to the “no extended hiatus” cause – the Ides “took a break” from 1973 to 1990.
I’m just remembering as I write this that one of the members of the Ides of March is an acquaintance of two of my bandmates. Outside of the Ides, Jim Peterik was in Survivor and co-wrote “Eye of the Tiger” and co-wrote hit songs for other bands, including “Hold on Loosely” for .38 Special and the theme to Heavy Metal with Sammy Hagar.
There’s a progressive rock band that I expect no one here has ever heard of called Djam Karet. They formed in 1984, all four founding members are still in the band, and they’ve released albums regularly over the past 25 years. It has been five years since their last album, though.
I too would have to mention “The Who”…“The Kinks” you mentioned “The Stones”…but also what about “The Beach Boys”?? They had been together a real long time. Lets face it…noone has really had all the original members non stop for all these years. Been some sort of hiatus. So, the ones I mention I believe qualify. Ray
Yes, “The Beach Boys” have Been together for 46 years or more, and still tour is some form or another. Ray
How about the Scorpions? No more lineup changes than the Stones and according to wikipedia “On January 24, 2010, after 45 years of performing, the band announced that they will be retiring after touring in support of their new album Sting in the Tail.”