In Episode 3, Yolei brings convenience-store food for the Digimon hiding out in school. Naturally, Hilarity Ensues.
Demiveemon: What is it?
Poromon: Can we eat it? I'm hungry!
Patamon: Of course you can eat it! Watch me! *takes a juice pouch and starts sucking on it*
Upamon: The buffet is now open!
Upamon dive-bombs the bag of food and starts stuffing his face, while Patamon falls over backward (still clutching his juice). Demiveemon is getting chocolate all over himself, and then Poromon takes a sip of juice and goes on a crazed sugar-rush flight around the room. The whole time, Gatomon is just standing there in the background with an epic "why are these guys such idiotic pigs" face.
Gatomon: *deadpan*…I hope my first litter doesn't act like this.
This becomes funnier when you realize that all four of the male Digimon have been shipped with Gatomon at some pointnote not as often with Armadillomon, but definitely with Hawkmon, Veemon, and Patamon, meaning the father of said "litter" is probably acting like an idiotic pig.
Also in Episode 3, in the English Dub one of Ken's many achievments includes "Being able to play one game of Chess while everyone watches"
When Yolei proclaims her triumph in opening up the Digital World on a Saturday, just then the door opens, and Mimi sticks her head in, asking if they're supposed to be there. The younger 3 immediately start panicking.
When Ken is defeated in episode six, he starts sulking.
Tai's cunning plan to distract the evil Digimon by TAP DANCING.
Daisuke (Davis) tries to get girls to swoon over him by changing his personality into … not telling. But a hint: the fangirls (no really!) are asking Ken his autograph, while Wormmon lines them up. Also, the dance floor is attacked and the Chosen use the others digieggs for a change. A translation.
Davis declaring himself as the new Digimon Emperor (Kaiser), only to have everyone (including the evil Digimon) boo him for being lame, and then have his best friend Ken (the former Kaiser) to mock him and show him how an evil overlord should really act.
A lot of Azulongmon's dialogue, but especially:
"The eight children and their Digimon were able to defeat the Dark Masters, but we were still trapped beneath the seal. In order to break the seal, we needed to take away the power from the DigiDestined crests. Of course, Joe complained about it, but he complains about everything."
He seems to make a lot of fun references to the Digidestined. Like when he told BlackWarGreymon, "You ask more questions than Cody does!"
When he talks about Izzy's intelligence, he remarks that "if he didn't have [it], he'd be...well, Tai!"
The mentions of a Power Rangers Arbor Day special and just the idea of such a thing existing.
Just the way Daemon says "You silly little imbeciles."
It's more of a Hilarious in Hindsight sort of thing, but one of the attack names in both the original and the English dub is called Rosetta Stone.
Paildramon: Do you even know what the word 'aim' means?
In episode 8, Miyako asks Daisuke for Ken's autograph, and Iori says that she'd said before she wasn't into younger boys. Miyako protests that her father is younger than her mother anyway. What's funny about this is that 42 episodes later it's revealed she actually did marry Ken!
An example not related to the animated series canon: the ''We Love DiGiMONMUSiC" disc for 02 has some of the voice actors for the main characters act out some joke tongue-in-cheek skits in-character. Romi Park (as Ken) and Naozumi Takahashi (as Wormmon) act out a scene where Ken and Wormmon try to find a good hot springs place to visit, but while looking, Ken finds one that happens to be a bit…"naughty". Hijinks ensue in which Ken attempts to keep Wormmon from looking, but the kicker is his final line:
In "Stone Soup," Mummymon is a hilarious Butt Monkey. Throughout the first part of the episode, he's trying to flirt with Arukenimon and ends up getting slapped. Three times. Later, after he accidentally draws the Destiny Stone out of the soup spring, he falls in the soup and starts drowning.
Mummymon: (choking) Help! There's a mushroom up my nose!
And how does Arukenimon help? She throws a giant rock at him to shut him up, and he goes under with the weight.
In "Ultimate Anti-Hero", the children are taking a break from destroying Control Spires by having some sodas. In middle of this, they are conversing about how Ken and Cody seem to be very distant from each other, especially since Davis's attempts at trying to get them to bond backfire. Then Davis says something that provoked nearly everybody to do a Spit Take and choke on their drinks. The line?
What about when the DigiDestined are stopped by a train crossing during a car chase, first one train passes, then another, then two at the same time, finally the entire car loses it.
Veemon: What is this; Grand Central Station?!?!?
Entire Car: (Chanting) Give us a break! Give us a break!
When Tai, T.K., and T.K.'s grandfather happen upon a French Digidestined named Catherine captured by Digimon, the younger two respond with an "All right!" The grandfather tells them to look below her, and they see a captured Floramon at her feet— to which Agumon and Patamon respond with a resounding "All right!" when they see it.
Skull Greymon's premiere rampage and Ken's failed attempts to reign him in with a battalion of BlackTyrannomon aren't all that funny. Kari's reaction, on the other hand....
Kari: Why can't we ever fight anything short?
Matt's scenes with Davis' sister Jun:
First, Matt goes to their apartment to try and give her an excuse for Davis' absence. While she's not suspecting of anything (or perhaps she doesn't care), she can tell he's lying. She then says that she's not gonna tell their parents, but in exchange, he'll have a date with her. Matt is terrified at the thought.
Later, she shows up unannounced when Matt, Tai and Izzy are ready to go on a camping trip (as a cover for the others). None of them wants her to tag along, so Tai tells Matt to do something. And while he talks to her, Tai and Izzy are clearly enjoying his misfortune. Since they're in a hurry, Matt finally tells her to turn around, close her eyes and count to ten. She happily does, expecting a surprise kiss or something, while Matt returns to the car and tells his dad to drive off and leave her behind.