If TV Tropes terminology is acceptable then I'd suggest "Once per episode" - http://tvtropes.org/pmwiki/pmwiki.php/Main/OncePerEpisode covers what you're asking about, with the sub-trope of "Every Episode Ending" - http://tvtropes.org/pmwiki/pmwiki.php/Main/EveryEpisodeEnding applying to your Bones example.
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The closest word I can find would be "staple".
One of the definitions of staple is "A main or important element of something", according to the Oxford English Dictionary .
As in, "The Captain's Log is a staple of Star Trek episodes".
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I would call this a "Recurring Plot Device ".
A plot device (or plot mechanism) is any technique in a narrative used to move the plot forward.
A contrived or arbitrary plot device may annoy or confuse the reader, causing a loss of the suspension of disbelief.
However a well-crafted plot device, or one that emerges naturally from the setting or characters of the story, may be entirely accepted, or may even be unnoticed by the audience.
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Every story should have 3 elements: Introduction (of place, characters, context) Conflict (show the problem, challenge)
Resolution
But when you're writing a series you have an established context, characters and place (in ST it's always USS Enterprise even when they go to different planets).
So you need to use thing called " hook ".
A thing that is more "exactly the same" than the characters.
The main difference between ST and Dangerous Minds for example are times they we're made.
In the ST:OS times it was though it would be good to put the hook at the beginning (A-team show same approach).
But, as some researchers propose, as the commercial brakes went longer it was though it would be better to place the hook at the end of the show so the viewer will have the feeling of watching homogenous thing.
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A motif .
Any recurring element that has symbolic significance in a story.
Through its repetition, a motif can help produce other narrative (or literary) aspects such as theme or mood.
For Star Trek
specifically, I always saw the Captain's Log as a motif toward the final frontier and continuous mission of space exploration.
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Each episode of  Star Trek  includes the captain's log.Each episode of  Bones  ends with a sweet moment between Booth and Brennan.Most episodes of  Criminal Minds  are bookended with quotes that are relevant to that episode.  Some TV series are written by a writing team, and others accept script submissions. As far as I know, all shows have a "bible." Is there a specific term for those elements that  must  be in a TV episode? If there is, what is it?
What do you call the required parts of a TV episode?
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<terminology>
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These sections could be called "staples". One of the definitions of staple is "A main or important element of something", according to the  Oxford English Dictionary . As in, "The Captain's Log is a staple of Star Trek episodes".  The most suitable word is staple
The most suitable word is staple: one of the definitions of staple is "A main or important element of something", according to the  Oxford English Dictionary .  