Contractual Gag

"Oh my God, they killed Kenny!"

"You bastards!"

—Stan and Kyle, South Park.

A Running Gag which may avoid wearing out its welcome but is always associated with a particular situation; the audience expects it whenever that situation comes up, but may not always find it as funny after a while. Removing the gag for a period of time will still make the audience ask where it went.

Usually not put in every episode, but frequently enough it becomes associated with the show as a whole. Writers may even start to make increasingly complicated setups for them just to keep the novelty.

If it's regularly being Lampshaded, then it's also an Overused Running Gag.

Live Action Television

In Home Improvement, Wilson's un-shown lower face became this. Originally, he just stood behind a fence on stage. As the show progressed, Wilson was shown out of the house more and set designers went to town finding ways to keep the portion of his face hidden with props. In all these cases, he was never shown, being obscured by at least three props in the scene as he moved around the set.
- Even at the final curtain call, actor Earl Hindman came out holding a miniature fence in front of his face (he did move it, though).
In The IT Crowd the apathetic Roy will always answer the phone with "Hello, IT, have you tried turning it off and on again?" In later seasons they progress to "is it plugged in?", and later still "I'm sick of saying that.. what do you WANT?!" It's worth noting that this advice solves, If My Calculations Are Correct, 72% of computer problems.
This was actually cited by Brent Gore as the reason he left the show California Dreams in its third season as his character had been reduced from the focus character of the show to a one trick pony who mostly showed up to whine 'Aww man' when things didn't go his way.

Western Animation

In Space Ghost Coast to Coast, Space Ghost would often abuse his Destructo Ray to blast the guest or Zorak when he tires of them.
Much Family Guy humor is based on Non Sequitur asides that play off the characters' metaphors. Occasionally, an aside doesn't happen, causing the character to flinch, "Oh? We're not doing one? Right?"
In Pinky and The Brain, Brain would often ask, "Pinky! Are You Pondering What I'm Pondering?" before a zany scheme, prompting Pinky to agree, before spouting a goofy nonsequitor.
- They occasionally turned it on it's head, for once Pinky thinking the same thing, then discarding it as too absurd, and another time they had an entire conversation about it.
- In one episode told from Pinky's point of view, the viewer sees his train of thought leading up to his non-sequitur, and it makes perfect sense.
Kenny's frequent deaths in South Park, one of the original hooks for audience attention. The creators quickly grew tired of the joke, however, and went to extreme lengths to lampshade or subvert the joke. They eventually left Kenny dead for a whole season, then brought him back and only killed him off occasionally. In a later episode, it's revealed that Kenny actually remembers being killed, but his friends don't. His mother gives birth to him again each time, and he matures to his current age overnight.
Phineas and Ferb is a show where the great deal of the humour comes from the formulaic plot and its Once an Episode running-gags and catch-phrases. To keep them fresh, the show will constantly tweak, rotate or make them pointedly absent in funny ways.

Anime

Many Megaton Punch gags are adapation of quick, one-panel visual gags. If Filler episodes use them just as frequently, it can make a character seem overly grouchy or abrasive. (Viz Akane Tendo from Ranma One Half.)