There are a number of situation comedy episodes that people cite as the funniest ever. I can't pick one but a worthy contender might be this episode of You'll Never Get Rich, aka The Phil Silvers Show, aka Sgt. Bilko. It was late in their first season that they gave us "The Court-Martial," sometimes referred to as "The Court-Martial of Harry Speakup."
I posted a scene from this back in 2006 but the entire episode is now online. Here's some of what I wrote back then…
It first aired on March 6, 1956 and the writing was credited to Nat Hiken (creator of the series and its main director and head writer), Arnie Rosen and Coleman Jacoby. I actually worked with Arnie Rosen on one of my first TV writing jobs and was somehow then unaware that he'd worked on Sgt. Bilko. Wish I'd known because I'd have asked him about it. Then again, he was more interested in pressing matters like writing the show we were doing and having me fired.
One of the many interesting things about the Bilko program was that even though it was done on film, they tried to treat it as much as possible like a live performance. They barely stopped filming between scenes and often, if someone bobbled a line or things went wrong, they left it in. There are a number of instances when actors — most notably Paul Ford, who was otherwise so good as Colonel Hall — forgot important lines and someone else — usually Silvers, who had a fast mind and a great memory — would ad-lib around the problem.
Silvers often improvised during the show and he had to ad-lib a lot in this because a trained chimp didn't always do what he was supposed to. At one point, the chimp ran over to grab a prop telephone and Phil came up with a terrific explanation right on the spot. His quick wit caused a few of the actors to almost break up. At several points in the trial scene, you can see some of them trying to stifle or hide laughter. Especially watch the kid at left playing a guard.
You probably won't be able to keep from laughing either…