In Bone, the insult "Stupid, stupid rat creatures!" is a Running Gag, as is one of the rat creature's fondness for quiche and the other's insistence that monsters should act a certain way.
Peanuts and its TV specials were fond of these, although always with some sort of variation. Lucy pulling the football away, Charlie Brown crashing his kite, etc.
Dagwood in Blondie: Always making his decuple-decker sandwiches, always running into the mailman on his hurried way out the door.
In Beetle Bailey, whenever General Halftrack sends his officers a written instruction, it will always have one tiny spelling error that completely changes the meaning of the orders ("buns" instead of "guns", "gag masks" instead of "gas masks", etc.). Someone will point out what the general meant to say, but then someone else will — always, invariably — ask: "But who dares to tell the general that he's done a mistake?" Nobody dares, and in the end, the officers always do exactly what it says in the instruction, even though it makes no sense. Often, General Halftrack is depicted witnessing the end results of his subordinates' interpreting his orders in some absurd way, and his reaction is always the same: "Now what?"
In Young Justice, whenever Robin would state the obvious, another character would say, "Obviously you've been trained by the world's greatest detective." If memory serves, even Batman got one in once.
Nikolai Dante encounters a seemingly unlimited supply of the Arbatov family; each of whom announce their intention to avenge the death of the previous Arbatov at the hands of Nikolai. Invariably they are themselves promptly despatched, to be avenged by later Arbatovs.
Groo the Wanderer has to be one of the kings of this trope: from defining "mulch" at every opportunity (or just randomly defining it for no reason at all) for five years straight, the titular character's ridiculous exclamations ("Hah! You take me for the fool I am!" "As any fool can plainly see."/"I can plainly see that!", "Groo does what Groo does best!", "Did I err?", etc.), ships sinking the instant Groo gets anywhere near them (unless his dog is with him), the name of the Sage's dog, Groo getting chased out of the city by every single person in the city, Drumm continually wanting to know "What pirates?" (and, later, alternating that with "You never bought me a house..."), Groo's dog never quite realizing how stupid Groo actually is, Captain Ahax going insane every time he's exposed to Groo (since the latter has a habit of continually sinking the ships under the former's command), "Must be stupid."/"Must be Groo."... and that's not even touching the 25 years worth of running gags in the letter columns.
Every issue also had a hidden message.
Also, whenever prompted to remember or not forget something, or sometimes just when he's got nothing to add to a conversation, Groo responds with "I am the Prince of Chichester!".
Thomson's and Thompson's introduction: "Thompson, with a p, as in Philadelphia [the p is never pronounced with a p sound], Thomson, without a p, as in Venezuela";
Captain Haddock's obscure "obscenities";
Snowy's alcohol problem;
The fact that Prof. Calculus is hard of hearing and therefore can never hear a sentence correctly;
Captain Haddock's inability of keeping his monocle intact;
Tintin and Haddock's inability to hide from Castafiore and her singing;
In The Broken Ear, San Theodoros' constant (once every 10 minutes at one point) revolutions, and a bumbling assassin's inability to kill Tintin;
Thompson and Thomson's tendency to dress in outlandish and completely out-of-place ethnic costumes in order to "hide undercover";
People trying to call someone and getting Cutts the butcher, or vice versa.
In a history of the making of Tintin, the author states that Snowy himself started as "a literal 'running gag.'"
In The Calculus Affair, Captain Haddock has a piece of sticking plaster put on his nose, and when he tosses it away, it winds up being passed around the entire plane before he finally chucks it out the hotel window. Referenced later in Flight 714 when Haddock says he had trouble with sticking plaster.
The Castafiore Emerald has several of these:
People constantly falling down the broken step.
"Hellooo - I can hear you!" / "Allo! J'écou-ou-oute!"
"MERCI! MY JEWELS!" / "CIEL! MES BIJOUX!
"No, this is not Cutts the Butcher." / "Non, Monsieur/Madame, ce n'est pas la Boucherie Sanzot!"
The hapless pirates get sunk once every issue. Sometimes twice. In one book, they give up the pirate life to open a (boat-shaped) restaurant. It gets trashed.
And every sinking is drawn to resemble, in some way, The Raft of the Medusa, a famous painting by Théodore Géricault.
Caesar's tendency to refer to himself in the third person. This was a reference to Caesar's Commentaries on the Civil War and the War in Gaul, where he constantly refers to himself in the third person, to the point that the reader can lose sight of the fact that Caesar isn't writing history but self-justifying propaganda.
The ways the village keeps Cacofonix from singing.
Obelix's constant attempt to get a taste of the magic potion.
Every time someone meets him for the first time, they inevitably comment that they thought he'd be taller.
This even extends to other members of the Batfamily, such as Dick Grayson (who, to be fair, is a good 4 inches shorter than Bruce, so it's obvious when he's dressed as Batman that he's shorter than the original guy) and Tim Drake (it's mentioned in Young Justice).
Dick Grayson (Age 12) has his own running gag. Guess which part of Dick Grayson (12 years old) is the gag.
Ever since Orient Men tried unsuccessfully to fix an Eskimo's broken radiator, the Eskimo kept following him all over the world and appearing at the end of nearly every episode, asking random bystanders whether they can fix his radiator.
A little background for this one: In Midnight Nation, it turns out that Lazarus Came Back Wrong, and was told by Jesus to wait until Jesus would return. Lazarus mistakenly thought that Jesus would be coming right back after having a little dinner with 12 of his best friends... that didn't work out so well, and 2,000 years later Lazarus is still waiting. So, the actual gag is that whenever someone around him says "Jesus" in reaction to something, Lazarus responds by asking, "Where?"
Artist Leinil Yu has been known to sneak Howard the Duck into everything he draws, especially during huge spreads with lots of heroes where Howard won't be as easily noticed. Nobody knows why except Leinil.
The DCU's Invasion! miniseries frames several of its scenes as television newscasts. Whenever a reporter tries to interview one of the heroes, the hero invariably replies with, "Get that @%&£$€# camera out of my face!"
Flax Seed: I always, like, feel like he's watching me. His eyes move with me. Always watching... never sleeping...
The Dutch comic De Generaal is full of these, with the most frequent one being a literal running gag: The eponymous general would always flatten the local cop's motorbike (and usually the poor guy himself too) under his tank or other Doomsday Device while on his way to the fortress he was forever trying to conquer. A later comic stated that the motorbike factory was "the cork that kept the Dutch economy afloat".
In the classic MAD parody of G.I. Joe, any woman who expressed a desire to talk to the hero would fling herself onto his lap and say, "Hey, Joe! You got chewing gum?" This gag resurfaced in at least one later Mad feature.
Superlópez: Any time Juan López enters a subway station, he'll absent-mindedly start ordering breakfast instead of asking for a ticket; then he'll go into a bar and order a ticket instead of breakfast. Sometimes it's because he's lost in thought, sometimes it's just plain stress or exhaustion.
Wiske is curious about something and brings herself into trouble by doing so.
Suske gets attention from other women and Wiske gets jealous.
Tante Sidonia getting a nervous attack and stiffening in shock.
Jokes at the expense of Sidonia's nose, thin body and large feet, usually by Lambik, who gets her shoe thrown against his head.
Lambik makes a Captain Obvious conclusion or says or does something else remotedly stupid. For instance he'll be master of a situation, but tricked into leaving or giving his gun to his opponents, allowing them to run away.
Jerom doing a remarkable stunt, showcase his superstrength.
Krimson getting a nervous attack and screaming for his pills, which are then brought by his butler.