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The first Tournament Arc, in which Krillin is able to fight a legendarily stinky opponent unhindered because he was drawn without a nose.
And then defeats him by farting in his face.
When Goku is telling Bulma, Yamcha, Oolong, and Pu'ar about the monster that killed his grandfather, along with destroying the surrounding landscape, he's asked what kind of monster it was. Goku replies that he didn't see it, as he was asleep at the time. Oolong's response is hilarious.
"You slept through your house being destroyed? What are you made of?"
When Chichi first meets Master Roshi, she can't believe such a pervy geezer could possibly be the Master Roshi, so she decides to test him by throwing her helmet blade at him. He fails, but convinces her by showing his drivers license. For the rest of the mini-arc, Roshi wears a giant band-aid on his head.
Add the time when child Goku tries to have a bath with Bulma.
And later that episode when Goku takes off Bulma's panties and discovers that her "balls" are missing.
And that's just the set-up for a gag later on. When they meet Roshi and discover he has a Dragon Ball, he says he'll only give it up if Bulma shows him her panties. Bulma reluctantly agrees and lifts her gown, not realizing she's not wearing anything underneath. It's not until later when they get back to the capsule house that Bulma finds her panties on the floor and has an epic meltdown.
And when Yamcha, who was in the worst stage of his fear of women, sees Bulma naked. His face is priceless.
Goku: Live together!? With you!? When I said this was I conscious!?
Of course, we all know he figures it out eventually. See: Gohan and Goten.
Jackie Chun's fight against Man-Wolf. It can't even be called a Curb-Stomp Battle, Man-Wolf is so outclassed. Chun wins by making Man-Wolf fetch a bone he tossed out of the ring.
When Pilaf has captured the heroes in the first Dragon Ball hunt, he has their cell gassed to knock them out. He then comes in to gloat... and passes out himself.
Right before Krillin's match against Jackie Chun, the announcer interviews both Turtle School kids. Afterwards, Chun wants an interview too, but the announcer refuses. So Chun takes his microphone and sings, with Goku dancing along. Watch here.
When Pilaf has Goku and company imprisoned, he reveals that their cell's glass roof is to slowly roast them in the hot sun.
Bulma: What do we do...?!! I didn't bring any sun block! Oh, my complexion!!
Oolong: You're not gonna die quietly, are ya.
When Goku goes underwater to search for a Dragon Ball, Bulma pulls out the capsule case and notices there’s only one capsule in there, and Bulma realizes she took her dad’s case. She decides to have a little faith in her dad and throws the capsule… but out pops a ton of porn. Goku thinks its weird how all these people have their clothes off even though they’re not taking baths, and she yells that kids aren’t supposed to look at that. She then tears up all the magazines.
Goku: This is weird... they're all naked, even though they aren't taking baths...
Bulma: KIDS AREN'T SUPPOSED TO LOOK THESE!!!!
Master Roshi using a watch that can shrink the person who is wearing it to spy on Bulma... only to arrive when she had finished and on top of that, falling into the toilet as Bulma flushed it. Needless to say, he stank very strongly after that.
Goku and Yajirobe playing rock paper scissors to determine which of them gets to fight Cymbal.
Cymbal: Oh, come on! That's not how you play. Everyone knows that dynamite always wins!
This bit of dialogue between Yamcha and Tambourine:
Yamcha: That must make you King Piccolo's yes-man.
Tambourine: Yes- I-I mean, uh, well you don't- shut up!
When all of the Dragon Ball gang are heading the city in King Piccolo is located to aid Goku and Tien in fighting him, Bad Launch for the first time shows eagerness and willingnes in fighting with the Dragon Ball gang against a major enemy, mostly due to the fact she wants to protect Tien as she loves him. Launch then suddenly sneezes, reverting her to her "Good" form, much to Dragon Ball's gang horror and disappointment and then asks: "Are we going on a picnic?"
Chi-Chi tries to drill Goku for an interview with a private school she wants Gohan to attend. She ends up yelling so hard at Goku that the entire line behind him falls down.
Early in Cooler's Revenge, Goku is suddenly interested in Gohan getting his schoolwork done, and is in fact insisting he finish it before anything else. Chichi, hearing this, concludes that this sudden Out-of-Character Moment is the result of brain damage.
In Trunks The Story, which was adapted into the Trunks TV special, Trunks asks Gohan to take him to fight the 'droids. Gohan's response? "Trunks! Look over there!"*smack*
Another hilarious Android 18 moment was in Bio-Broly when she basically shows who's the dominant figure in the household.
Android 18: Now do as I say and wait at Roshi's house. Krillin: No, I'm coming with you. Android 18: You look after the baby. Krillin Aww, but 18! Android 18: Why won't you simply obey me?!
Krillin, naturally, follows this up by dropping the baby off somewhere safe and ignoring her orders completely. Because he was worried. Which is fairly funny as well, if the nature of the relationship was that she gives orders and he just decides to follow them or not based solely on being a Nice Guy. It's like a twisted, almost heartwarming fusion of Goku and Vegeta's relationships with their wives. No wonder she always seems content yet annoyed with him.
Well, okay, it's "obey us" but really, this is the closest thing DBZ will ever get to "Pingas".
In "Fusion Reborn", when Goku attempts to convince Vegeta to do the Fusion Dance as the former is just newly revived and the latter is dead and both are fighting a very powerful demon who's kicking both of their asses...
Also from "Fusion Reborn", the group summon Shenron to return all the souls to the other world, however he explains that he can't as there are no barriers between the worlds to keep them there. The group seems to ignore Shenron for the rest of the movie, and at the end...
Shenron: Uh... Don't you people have any more wishes?
The best part of that, nobody bothered letting Shenron leave so he's still stuck waiting for somebody ask for a wish at the end of the movie.
"Is someone going to make a wish or what?"
Vegeta meeting Gure in the 2008 web special. I should mention that the character being discussed, Gure, is a 2-foot, dot-eyed, dress-wearing alien with gray skin, while Tarble is a normal-looking Saiyan.
Vegeta: Tarble, who is this with you?
Tarble: Oh, sorry. This is my wife.
Vegeta: *looking like his eyeballs are about to beat a hasty retreat from his skull* Your WIFE!?
Gure: *runs up, smiling cheerfully* How do you do, brother? Nice to meet you! *bows* It's an honor!
Vegeta: (totally catatonic) *bows* Oh, no... the honor's mine...
Vegeta: Not until the fish jumps. *fish jumps* It's over.
Ladies and Gentlemen, I present to you: Vegeta, the Prince of Saiyans. Dancing.
Beers's reason for wanting to destroy the Earth in Battle of Gods: Boo eats all of the pudding when Beers wants a taste of it. Beers completely snaps and decides that he has had enough of this pathetic world.
The Pilaf gang's reaction to Trunks admitting his fib (paraphrased):
Trunks: Um... I made up a story and now I need you to pretend to be my girlfriend.