Some of Thompson and Thomson's slapstick moments qualify; in the first episode, they step through the cabin door of a ship and one of them bashes his head on the top of the door frame — the first mate tells them to mind their head, and the other responds with "Mind my head, of course.", ducks ... and trips over.
At one point, a photo of them falling down the steps in an attempt to apprehend the criminal is used in a newspaper article about the event, complete with Comically Serious caption.
The Thompsons' crowning moment has to be their Outdated Outfit appearance in The Blue Lotus.
"Don't look now, but I think we're being followed."
The entire sequence in Destination Moon where they think there's a live skeleton walking around the complex. So they arrest and handcuff the skeleton in a doctor's office. The doctor is not amused.
The bit from Red Rackham's Treasure where Thompson and Thomson try to help with navigating. After reading the coordinates they give him, Captain Haddock tells them to remove their hats and pray. They do, and enquire why. The reason? "According to these coordinates, gentlemen, we are currently standing inside Westminster Abbey!"
Whenever Captain Haddock loses his temper.
The time he doesn't lose his temper, and is faced with a reporter from the newspaper that had leaked their treasure hunting intentions. Instead of chewing the man out, he asks that he interview his secretary: Professor Calculus.
When Calculus is discovered aboard the ship, leading to the Who's on First? exchange culminating in "Separate pieces? My whiskey is in separate pieces?"
And when Haddock does lose his temper, some wonderfully creative insults are on their way.
The Truth Serum-induced Eviler than Thou bit in Flight 714. It was also even funnier in the animated adaptation where after Haddock tapes their mouth shut, he says "I'M the baddest." Tintin then says that this will make an interesting story.
Rastapopulous's Villain Decay is driven home in this book when he swears that he's going to crush Tintin and his friends "like this spider"...only for the spider to continually dodge his attempts to squish it.
In a conversation with Calculus in Tintin and the Picaros, Tintin and Haddock repeatedly end sentences with words that sound like "sister", leading Calculus to get increasingly annoyed: "And for heaven's sake would you stop talking about my sister!" He then thinks for a moment and remembers that he doesn't have a sister, before storming off in a huff anyway.
Snowy tried to steal a dinosaur bone from a museum in King Ottokar's Sceptre.
In the same comic, Tintin and Snowy had to hitch a ride with Bianca Castafiore to the Syldavian capital, and she decided to "treat" them to her music.
The Sticking Plaster Running Gag in The Calculus affair.
The Castafiore Emerald has so many in the form of Running Gags and Brick jokes.
The step never being fixed until the end...wherin it is completely destroyed again.
The mason shown as being lazy.
"Helloooo! I can hear you!"("Allo! J'écou-ou-oute!")
"MERCY! MY JEWELS!"("CIEL! MES BIJOUX!")
"No, sorry this is not Cutts the Butcher".("Non, Monsieur/Madame, ce n'est pas la Boucherie Sanzot!")
This one isn't a running gag, but there's something hilarious about the Paris-Flash tabloid proclaiming the betrothement of Haddock and Castafiore. One of the photos shows Haddock scowling murderously at Iago the parrot, accompanied by the placid caption "He opens his heart to the parrot she gave him."
After putting up with Iago imitating Bianca Castifiore he tells it to change the record after she's gone, whereupon it scares him by bellowing "BILLIONS OF BLUE BLISTERING BARNACLES, SHUT UP WHEN I'M TALKING!" in his face.
The remarkably surreal scene where Calculus' attempt at color television.
From Red Sea Sharks:
Castafiore comes to greet the rescued Tintin, Haddock and Skut. Haddock's (perfectly serious, slightly panicky) reaction: "Do we get back on the raft?", followed by this dialogue: "Ah, and Captain..." "Harrock, madam. Captain Harrock'n'roll!"
When what turns out to be a slave trader boards the ship (thinking Hadddock is the regular captain), Haddock kicks him off the ship and continues yelling his trademark insults after him, until Tintin points out the slaver is out of hearing range. Haddock then gets a megaphone and continues to rain insults until definitely out of range.
Policeman: (sweating bullets) Er, just don't do it again, will you?
The Italian zooms off.
Italian: Now we catch up on the time we missed!
In one comic, Haddock's in the bath when the phone rings. He has the detachable shower head in his hand, and mistakenly puts it up to his ear instead.
Tintin, Haddock and Snowy getting drunk off wine fumes in The Crab with the Golden Claws:
Haddock:(chasing a villain) Blackamoor! Anthracite! Coconut! Fuzzy-wuzzy! Cannibal!
Tintin: Go on! Seek! Seek! Bite him!
A bit of Black Comedy at the end of Picaros, when Tintin gets the favor he asked of Alcazar for his help: That nobody, not Tapioca's troops, not his ministers, not even Tapioca, be shot. Made particularly hilarious by Tapioca begging that they spare him the horrible fate of being spared. He and Alcazar share a moment when they comment on these idealistic young people, what is the world coming to...
When the group's tent is blown away in Tintin in Tibet, they hear the yeti roar, then a crunch, and next we see it squealing in pain, having run into (and denting) a boulder.
Also his freak out when he thinks Bianca Castafiore is in the next tent (It's actually the radio.)
Haddock: Bianca Castafiore! She's HERE by thunder! That woman follows us to the ends of the Earth!
From the cartoons
In Nelvana's Animated Adaptation of The Land of Black Gold, after Abdullah tricks Dr. Müller into crashing his car into the sand, he points a (toy) gun at Dr. Müller, as the car smolders in the background, and demands...ice cream.
From "The Crab With The Golden Claws":
Thomson and Thompson: (together) We think you're smuggling drugs!
Omar Ben Salaad: BY THE BEARD OF THE PROPHET-
Ben Salaad's henchman, Allan, emerges from a hidden bookcase entrance leading to their opium cellar, and proceeds to crush Ben Salaad behind the bookcase in the process
Allan: RUN FOR IT, OMAR!
The scene in The Castafiore Emerald where Professor Calculus' color TV undergoes glitches during a demonstration translated pretty well to animation. They also added a gag in which either Thomson or Thompson discloses that they brought the gypsies' monkey in for interrogation, but he hasn't answered any of their questions.
Thomson and Thompson come to the house of a pickpocket. He thinks they've come to apprehend him, when really they've come to return his wallet. They spend most of their time there babbling amongst themselves while the pickpocket confesses to his crime, and the contrast between their conversations just... makes this scene.
Especially when they are seeing the wonderful collection of stolen wallets the robber has, and they believe they are all his, finding like six or seven of theirs... and still believing they are the pickpocket's, while the man is still confessing and they aren't paying attention.
Pickpocket: I'm a kleptomaniac.
Thomson: What's that?
Thompson: Someone who's terrified of open spaces.
Thomson: Oh. That would explain why he keeps all his wallets in the living room.
They don't even get the hint after finding their own wallets! (Or the wallets of each other, hard to tell with those two.)
After Tintin buys the Unicorn in the market, Barnaby approaches and offers to pay him double. This annoys the man Tintin bought it from, not least because Tintin had already haggled him down to half price. It only gets worse when Sakharine appears. "Ten years I've been flogging bric-a-brac and I miss 'name your price' by one bleeding minute!"
When Haddock prepares a lifeboat to escape from the Karaboudjan, he's confronted by a crewman with a gun, who had been sleeping inside it. Haddock is told to put his hands up, and he does - letting go of the rope in the process, dropping the boat out from underneath him and leaving him dangling from a loop hanging off the side.
Allan: Mister Tin... (pauses to read paper) ...tin?
Tintin going through the trouble of going into a room full of sleeping crew members (which is already funny enough as it is) to get a key which Haddock uses to open the door to a room stocked with whiskey. Tintin's utterly deadpan expression in the background is priceless.
Near the end:
Sakharine: Do I pay you to talk, Nestor?
Nestor: You don't pay me at all.
So Tintin and Captain Haddock are in a plane that's being thrown about in a storm, and Haddock, desperate for an alcohol fix, spots a bottle of medicinal alcohol. He tries to drink it just as the plane lurches downwards, resulting in the liquid floating out of the bottle in zero-gravity, which Haddock proceeds to slurp up. And then Tintin tells Haddock that the plane is running out of fuel, and that Haddock has to refuel the plane manually. While it's still in the air. With the alcohol he just drank. So he climbs out of the flying plane and belches into the engine, reigniting it with alcohol fumes from his breath.
Every single moment Thompson and Thomson are on screen.
Tintin: Congratulations, Captain. You're sober. Haddock: SSSSSSSSSSOOOOOOOOOOOBBBBBBBBEEEEEEERRRRRRR.......... (The word continues to echo faintly)
Snowy is chasing a car that Tintin has been chloroformed and stuffed into. He ends up going through an enclosure full of cows, brushing up against the udder of the first cow. The cow responds by raising its head and mooing loudly in shock. Cue a trail of cows raising their heads and mooing. A very Spielbergian way of showing things.
The pickpocket gets hit on the head, and we see Circling Birdies, like you would expect if this were a comic or a traditionally animated cartoon. Then a guy with a net appears and catches the birds... It turns out that they escaped from the nearby pet shop!