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The multi fandom crossover series, Chance Encounter has a couple of these.
One is Balian a) insisting 'it feels worse than it is' or variants thereof b) Balian's numerous attempts to escape whichever infirmary he is in this time, being something of the Butt Monkey (he gets beaten up repeatedly, usually after doing something stupidly heroic and getting outnumbered).
'Nanny Balian' and 'Nurse Legolas' (or according to Jack Sparrow, Nurse Legless, somewhat ironic as he spends most of his time drunk). This last one also doubles as a Berserk Button for both of them. Also, 'Truly, it is not a coincidence' or some variation on the theme, however this can be seen as arc words, referring to divine meddling. The author is rather fond of the phrase, using it in a separate but similar fic.
Rainbow Dash blurting "Hey!" when meeting Phoenix and Twilight before the trial sessions, startling them.
Twilight's poor tree home/library can't stay in good shape for more than minute after it's repaired in Ponyville Goes to the... Dragons??. As of fourteen chapters in, it's been wrecked by a spell gone wrong, had it's books scattered around the place more than once on accident, had it's front door knocked off it's hinges repeatedly, completely decimated by Cynder's tornado attack, and has had multiple fights break out in it. Needless to say, this get's repeatedly lampshaded.
Xander wishes God would just kill him before he becomes like Angel (Xander is mentally 26, physically 16, and has several teen super-heroines interested in him)
In Origin Story, everyone assumes that Alex Harris's name is “Karen Starr” (which is Power Girl's real name) despite her never once claiming to be Karen Starr. And no one really believes her denials, either.
Dragon Ball Abridged has the Krillin Owned Count, which is fairly self-explanatory. Prior to Episode 25, he has been owned 14 times. Frieza then bumps him up eleven more for a total of 25 (and two 1ups to boot).
For the Planet Namek arc, virtually everything referenced that should be alien simply has "Space" tacked on in front of an Earth reference.
Be the Sea Dweller Lowblood has... no, the OTHER sea dweller lowblood. No, not that one! The OTHER other one! The FEMALE sea dweller lowblood! No, not that female! Seriously, you're just doing this on purpose now.
Sea dwellers don't have hearts. They have collapsing and expanding bladder based aquatic vascular systems.
Alternian Turnabout: Aradia Megido: This fangame continues running gags and callbacks from Ace Attorney, Jailbreak, and Homestuck alike, ranging from the old ladder vs. stepladder discussion to the vanishing pumpkins.
In the Mass Effect self-insert Mass Vexations, Author Avatar Art introduces The Game to Urdnot Wrex. There isn't a single conversation that they have afterwards where Wrex doesn't try to make Art lose the game.
And, as of MV2, Wrex has taught ALL OF TUCHANKA about the game. ALL OF IT. Art loudly makes Wrex lose the game and the entire room of Krogans goes "Oh, dammit!"
Mega Man: Defender of the Human Race has the author asking fans to point out any continuity errors big enough to [x], with [x] usually being something near-impossible, such as breaking a Met's hardhat.
Progress has poor Princess Luna getting bashed and battered by baseballs. That, and her attachment to her abacus, which has become a bit of a running gag in itself because it gets shout outs in other fan-fics.
Ponies The Anthology has several clips that repeat throughout the entire show, but the best known would be several characters "Firing their lazor." Throughout the first Anthology it's done with Fluttershy, Pinkie Pie (twice), Spike, and, somehow, a letter to Princess Celestia.
Boy Scouts ˝, set in Massachusetts, almost completely ignores characters from the original work. The one major exception is Ryoga, who invariably turns up once a storyline, lost and wondering how to get back to Japan.
The gag is turned on its head in the sequel series Boy Scouts ˝ in Japan. When Ryoga sees the Boy Scouts ˝ characters, he assumes he is in Massachusetts once more, failing to notice that this meeting is taking place right outside of his intended destination. Poor Ryoga wanders away before anyone can inform him of this.
Brandon getting knocked out in Pokeumans. Dropped in recent chapters, but at his peak he was going about five times per chapter.
In Pokémon: The Mew-sical, there are several running gags, including Giovanni shooting people, James trying to work the Magikarp submarine into every plan, and Gary ordering Eevee to use Leer, following the command with "SICK!"
When the four first meet the exiled skahs wizard Lyndess, she immediately asks them, “What are you selling, olyrr-sars [outworlders]?” When they are sent to Ta'akan, every single person they meet thereafter asks them the same question, until word finally spreads that they have nothing to sell. (At one point a very annoyed John comments that if they get asked that stupid question one more time, he's going to pull his trousers down and say “Yeah.”) Much later, when the Hunter is brought to Ta'akan, he gets swamped with people asking him that.
There's a literal Running Gag that starts in the New Zork chapter. Ringo finds himself yanked, dragged, and carried around by practically everyone he meets. This includes a pair of disembodied arms that throw him off a roof, Beagle Brian Epstein, some cops, Flyboy from the “Hitler Youth,” and John. He gets picked up and carried in someone's arms several more times during the book (including twice during the climactic assault on the warehouse), and at one point the Hunter offers to carry him.
Three in Breakaway, all in the protagonist's team:
Ice's ignorance of mainstream culture, idioms, and informal English.
Windy: "Does the word 'ain't' not register in your vocabulary?" Ice: "Should it?"
Windy constantly teasing Ricki and saying things like "green-blooded hobgoblin," as if they really wereMcCoy and Spock, respectively.
Which leads to the final running gag: the girls constantly roleplaying Star Trek.
The CSI fic What if Our CSIs were on Facebook has a ton, because it's a parody. Each character has at least one: Nick says he looks hot doing everything. He also often wets himself. Gil always says stuff makes him nervous. Catherine wants Warrick to take his shirt off. She also often forgets she has a daughter. Catherine's dad, Sam, often mentions his concrete swimwear. There's also a running gag about the writers being cheap because of the Lawrence Fishburne Emergency Contract Fund, and one about the show being set in Vegas but filmed in LA. Then there's the Tarantula gag, which turned into two versions-Gil G and his literal tarantula, and as a euphemism for a certain body part, for multiple characters. Later events like Nick being buried and Warrick being shot turned into running references too, way before they happened.
Naturally when 'Ending Happy' rolled around, the author got as much mileage out of the 'no signs of sexual trauma' running gag that was shown onscreen as possible. (Dave:Still no signs of sexual trauma!)