Slayers is a comedy series, but for a Crowning Moment..."Koala"
Explanation for the unintiated: Early in the first season, Lina and Zelgadis, the latter just undertaking his Heel-Face Turn, are on the run from Rezo when Lina gets blasted and sent flying face-first into a tree. She latches onto it and then turns her head to face the audience, mimicing the common depiction in Japanese media of a koala, and dopily declares "Koala", before Zelgadis grabs her and yanks her to safety.
Episode 25 of the first season. The group is in a serious battle against Copy Rezo. Lina had been seriously injured, and Sylphiel had taken her somewhere safe to be healed. The mood shifts radically when Prince Philionel comes charging in on a white horse to attack the villain. Cue UNBELIEVABLE looks from Gourry and Zelgadis.
Zelgadis: Well, they can't let these episodes be serious for too long.
Next episode 14, the girls learning "Otome no Inori". This is mainly one for the dub (You can't blame Lina when she yells "IN JAPANESE!" before the actual song — Zelgadis was singing better than both girls!), but Zel's delivery during My heart's beating so fast inside my little breast~ in particular.
Episode four of Evolution-R, which begins with a fish-woman who claims Gourry's her husband and the father of her spawn and gets progressively wackier from there, parodying a long list of soap opera cliches.
Zelgadis: [After being glomped by the fish-woman's daughter] ...Don't touch me there.
From episode one of Evolution-R:
Lina: Even beautiful roses have thorns... just like me!
*Cue retching from everyone else*
In the very beginning of NEXT episode 18, Xellos is looking at a tablet stating that it's a wishing spring, and if he throws a coin in and rings the bells, good things will happen. The instant he rings the bells, they fall on his head. It comes out of nowhere, and it's hilarious.
Gets Hilarious in Hindsight the following episode, when Xellos' nature as a demon is revealed and you realize that yes, a good thing did happen.
This one's a novel exclusive — in the first novel, during the scene when Lina wakes up captured and is now forced to sit through whatever petty revenge Zolf has lined up for getting the better of him with that light spell/Fireball shenanigan, Zolf decides to really gross her out and tells Noonsa to kiss her. Noonsa comments what a lucky girl she is — he's considered one of the choicest mates in his school. Then he sits and waits patiently. Finally, someone asks Noonsa what he's waiting for. "The eggs," he replies; all he really knows about kissing is that mating comes into it somewhere.
In episode 4 of Next, the four are arguing in the middle of the road, and every citizen is around them as if a dramatic fight is going to happen. And when it turns out they are arguing about restaurants, the crowd disperses.
When Wizer Freion shows up to arrest Lina, he's asked on what charge. The charge? Being Lina Inverse. And the best part is that Lina's friends admit it's a terrible crime!
About halfway through Next, at the end of the Ragna Blade mini-arc, a Floating Island is falling on Seyrune and Lina Inverse steps up to hopefully blow it to bits with a Dragon Slave. Amelia, as Princess of Seyrune, promptly addresses a prayer to Shabranigdo begging him to save the city. Cue Zelgadis angrily telling her not to pray to Dark Lords, while Gourry confusedly asks if Amelia isn't a Shrine Maiden, while Amelia sheepishly defends her actions.
For those confused; Amelia is a self-professed Love Freak for Justice and a professional White Mage. Shabranigdo is the Ultimate Big Bad of the setting, in that he is the God of Evil itself (the Dragon Slave draws upon Shabranigdo's power, hence why it's the strongest Black Magic spell in the setting).
From the first episode, an old man explaining why Lina is nicknamed Dragon Spooker: it means that dragons step past out of clear revulsion. And later in the episode, a dragon does just that. Said dragon is disintegrated (along with the town) soon after.
In one of the movies, Lina was about to be attacked by an horde of dragons, and their handler asked her to present herself. Lina says her name, and, as the handler declares she knows about her but she'll squish her anyway, the dragons realize in horror who they're facingand fly away.
The aftermath of Noonsa the giant fish-man's death (via getting fried by Zelgadis.) After Dilgear and some equally non-human henchman mourn his death, Rezo appears to Dilgear to tell him who the culprit is...and the other henchman eat Noonsa while he isn't looking.