As far as longevity is concerned, I guess the Stones do hold the record (provided they can be considered "not broken up"). The Grateful Dead came close, but then Jerry Garcia died. KISS is still around, though since they're currently on a "Farewell Tour" it seems likely that if they do make it to the 30 year mark (2004 I think) it'll be the end anyway. Besides, KISS has a problem keeping their lineup the same. AC/DC's been around quite a while, but it's not really the same since they had a lead singer change (drug overdose).
It still blows my mind that groups I grew up with are celebrating decades. They Might Be Giants started in 1982, Bad Religion's been around slightly longer, and GWAR even has longtime fans bringing their kids to the show now. Hell, the grunge music I listened to in High School is over a decade old now. When I listen to Appetite for Destruction, I start to feel old.
The other end of the spectrum is the "burn out" artist. Jimi Hendrix recorded for four, maybe five years, but to this day new material is released. The man must have never left the studio, except of course to die of the occasional overdose. Perhaps if Led Zeppelin had not broken up due to the alcohol related death of drummer John Bonham they might have gone south and released imperfect albums - as it stands now their nine studio albums are still brilliant. Had Lennon not been killed we might have seen Beatles reunions and that group would have not enjoyed the legendary status they do now. The Eagles seem less mythical since we know they got back together. Like Denis Leary said, had Elvis died in 1958 we would have been spared the polyester jump suit years.
Therefore, the fact that Aerosmith is still here, still kicks ass, and still has the original lineup is all the more impressive.