It seems to me that I recall a woman who’s voiced the same Warner Brothers cartoon character for 70 years, or something extreme like that… I think that the character was an old lady? Can anyone remember who it is I’m thinking of?
June Foray, again. She did Granny and Witch Hazel. She did Witch Hazel from 1956* to 1996’s Space Jam and Granny from 1955 to 2014**
*Although she voiced a different Witch Hazel in 1952 in a Donald Duck cartoon
**Granny appeared earlier, but voiced by different actresses, mainly Bea Benaderet
Don Hastings played Bob Hughes on The Edge of Night for 50 years, from 1960 to 2010 (when the show went off the air).
Hastings appeared almost continuously (two six-month gaps) on one TV show or another from 1947 on.
Moe and Larry of the three Stooges were characters played by Moe Howard and Larry Fine. They weren’t playing themselves, although they may have shared some personality characteristics with the characters.
Buddy Ebsen started playing Barnaby Jones in January 1973 and reprised the role in the horrible Beverly Hillbillies movie of 1993.
Only 20 years, but considering the man’s age at the time, he deserves some credit! 
They’re “playing themselves” at least as much as Groucho or Burns, though, which is where the OP drew the line.
As do Bob Newhart and Suzanne Pleshette. Who’d’ve thought they’d still be playing the Hartleys in 1990, twelve years after Bob’s first series was cancelled? :dubious:
Desmond Llewelyn was James Bond’s Q for 36 years. Not the longest period, but it is more or less continuous, without the long gaps in some of the suggestions.
Bonus points to Anthony Daniels, for showing up in the prequels like they didn’t.
William Shatner played a lawyer character in “The Defender” (an episode of “Studio One” in 1957, and this character was repurposed as the younger version of Denny Crane in an episode of “Boston Legal” in 2007 in an episode that used the original footage as flashback material.
…starts Kickstarter funding for 2040 release of Star Trek XX: The Wrath of Wesley Crusher…
I discount them fore a different reason. They were different characters in almost* every movie. In one they were surgeons named Howard, Fine & Howard. In another they were fishmongers named Hook Line and Sinker. Different names, different background, not the same character.
*I believe there was one where they reprised the same characters from an earlier film.
Peter Falk started his iconic run as COLUMBO in the '60s, and was still at it in the '70s, and kept plugging away at it in the '80s and the '90s and the '00s.
But the same is true of Groucho. While he was always doing the same sort of Groucho schtick, just as the Stooges were always doing Stooge-type schtick, each of Groucho’s characters had different names and often different professions.
Edited to add: I guess that I’m agreeing with you, as I finally realize that you’re arguing against including the Stooges, not in favor of including them.
Add a year onto that for Newhart’s 19th anniversary special in 1991.
Yes, and just to clarify I regard Otis B. Driftwood, Rufus T Firefly, Captain Spaulding, etc, as different characters too.
I read somewhere about a curious feature of American soap operas. Characters will have children, who then age rapidly into teen and young adult characters (so they can be part of the storylines typical of soap operas), and then have children of their own. The result is that certain generations (and actors) tend to cycle through much more quickly than real life. However, soaps also tend to keep their family matriarch characters (and actors) around for decades. If you map out the family trees, it turns you have characters interacting with their great, great, great, great, grandchildren.
Not sure if that’s true of British soaps as well?
Burt Ward let slip that DC is producing an animated movie starring himself and Adam West as Batman and Robin based on the 1966 TV show and set for release in 2016. So that will make 50 years for those two playing the same characters. Julie Newmar is also rumored to play the Catwoman.
YES!!! Yes, yes, yes, yes!!! 
William Roache has been playing Ken Barlow in the Brit soap opera “Coronation Street” since 1960, and is still going. 55 years…