This is a good question...not sure how to answer it.
My D&D 5e game has several characters and elements from my old AD&D2e game in it, so technically it would qualify (though they are background characters and nothing more). That would be about a 20 year span, though certainly not uninterrupted.
My Marvel game started in '95, with Marvel FASERIP and ran on and off until a couple of years ago...but again, lots of interruptions.
A Deadlands game that I started off as a player in, but then took over a Marshal, was still going as of last year.
The longest continuing game that had a solid beginning and ending would be Necessary Evil, which took us about four years to get through, but again, lots of interruptions.
These days, my current group aims to end campaigns in a timely fashion, with about a year being standard.