Faithfully done in the Batman: The Animated Series episode based on the one-shot comic.
The Batman Adventures: In Mad Love, where Harley Quinn tries to explain the deathtrap she built for Batman and how it is humorous (thus meeting Joker's standards for Batman having a hilarious death), but it backfires - partly due to this trope and partly because of Joker's conviction that he is the only one allowed to defeat Batman.
During the roast of Bob Saget, Norm Macdonald did this with lame and predictable jokes, turning his roast into a Post Modern mockery of roasts themselves.
A common "gag" is one character blurting out a non sequitur and another character shouting "THAT DOES NOT MAKE ANY SENSE!" For more information, see Boke and Tsukkomi Routine.
Japanese humor can have a lot of this.
Subverted by Craig Shoemaker who will find a young person in the audience and explain the older jokes (like his Barney Fife impression) to them, making age jokes at their expense.
Also helps to SPEAK VERY LOUDLY, in case they don't understand English in a normal (i.e., amplified through microphone) tone. Examples include Steven Wright (who already has a notably slow delivery), Ron White, Jimmy Carr, and Daniel Tosh (his trademark involves explaining a particularly complicated or obtuse joke).
Many stand-up comics use this as part of their act, especially to single out a heckler to explain the joke very slowly to them.
Nerina: You'd appreciate this: number two's quite cute, isn't he?
In Dragon Ball, when the Ginyu Force meets the unlikely alliance of Gohan, Krillin, and Vegeta, Ginyu decides that he and his men will "play" with the heroes (and Vegeta).
Justified because these are, in-universe, seen as exceptionally obscure and only funny to manga enthusiasts.
In Bakuman。this sometimes happens with the more obscure manga references, such as one in which Nobuhiro makes a reference to the little brother of Sally the Witch.
Black☆Star of Soul Eater sometimes overexplains the meaning of his jokes.which is necessary, because they're pretty incomprehensible.
Pokémon's dub is absolutely rife with bad puns, and sometimes lampshades this: "Looks like I'm all in one.PEACE! Haha, see, it's funny, because I'm making a 'peace' sign!".
At the end of this segment, Hyatt chimes in, noting that it's already a musical (with Hyatt's enigmatic personality, it may be variant 4 or 5, though). They conduct this argument while singing the melodies of the series' music.
In the beginning of the 26th episode of Excel Saga, Excel has an argument with director Nabeshin about making a musical episode (musicals, after all, take a lot of effort to produce).
It gets to the point that the caption itself is its own Running Gag. Every single time this occurs, there's a little caption box that says something like "Miu has a habit of throwing anyone standing behind her".
Kenichi: The Mightiest Disciple has a Running Gag that if anyone comes up behind Miu, she'll throw them.