How much you like the later seasons depends on your tolerance for Levitt, I think.
Timmy tried and failed to Jump the Shark that was in a well, but Lassie saved him.
I’m not sure that a 13-episode adaptation of a novel and its sequel is quite what the OP meant by “long running tv show”.
And I’ll second Arrested Development, at least if you can consider 3 seasons to be “long running”. IMO, it definitely ‘grew the beard’ when it evolved from a fairly standard, if well-acted, awkward-comedy sitcom to a work of absurdist brilliance. Which I think happened somewhere in season 2.
Both “Twin Peaks” and “Crime Story” were excellent in their first season and pathetic in their (mercifully abbreviated) second seasons. The problem was that the basic conflicts were resolved in the final episodes of their first season, and with them went the whole premise of each show. I mean, where can you go from up except down?
Most of the shows that never jumped the shark (MTM, DVD, “Cheers!”) had the good grace to exit voluntarily while things were still going well, and the story possibilities had yet to be exhausted.
On TVTropes, it’s TrippyFinaleSyndrome, shading into GainaxEnding if it’s incomprehensible.
The Prisoner got nuts* during development.* I think McGoohan wanted weird, weirder than some of the writers expected. But does that count as Jumping the Shark? I’m gonna say no.
I’m going to go against the prevailing opinion on SDMB and say The Simpsons. There are still quite a few scenes and entire episodes that are hilarious.
Boston Legal was good to the end.
Adam-12.
Actually the problem with “Twin Peaks” is that it didn’t resolve the basic conflicts in the final episode of the first season. Everything leading up to it promised a spectacular resolution to the “Who Killed Laura Palmer?” question, and instead we got no answers and a new “Who Shot Agent Cooper?” question. It was like a big “fuck you” to the fans, and they duly abandoned it the next season.
And this is why I never bothered watching “Lost” after the first few episodes, when it became obvious that the entire series was going to be like that.
I don’t think COLUMBO jumped.
I’ll call your Adam-12 and raise you Dragnet. In both cases, it’s hard to jump a shark when every episode is practically identical to every other episode.
Any takers on Monk? It had some ups and downs but seemed pretty good over all to me.
I thought Star Trek: Deep Space Nine did pretty well – it had the occasional bad episode/arc (coughEzri) at any given point during the run, but the last couple of seasons as a whole were awesome.
Pulled off the gorilla mask?
I agree. And while the final episode was strange, it was far better than a more mundane explanation.
Now, the remake jumped at minute 1, when Number 6 saw a guy with a real Number 6 jacket. It sank from there.
I saw all of Danger Man/Secret Agent, including the early 30 minute episodes, and it only jumped at the final 2 or 3 color (sorry, colour) episodes. And I’ll say that is almost a non-jump since McGoohan then jumped ship. If you consider the Prisoner a continuation of Secret Agent, then it would be a massive and quick un-jump.
I don’t think he bathed either 
The Twilight Zone
I loved Perry mason as a child.When I read the stories as an adult I found all the tv series and the books had in common were the titles. There was very little connection. On the side, I found a 1930’s version of Perry Mason that presented a young Errol Flynn (non-speaking role) as the victim. Sorry about the hijack.
ST:TNG must have ended too well since the-powers-that-be sent Ryker over to ST:Enterprise to jump their shark.