Mikoto's frenzied run throughout Fuuka Academy in search of water after eating curry bread in episode 2. It happens again in episode 8 after she eats some spicy ramen.
The Omake for episode 3 is styled as a promotional video for Fuka Academy. It's introduced by Mashiro, and shows various scenes of the idyllic life and academic opportunities at the school... and the occasional monster or fiery explosion, which quickly turns to static (as if they just realized they shouldn't be showing people that).
Episode 4:
Natsuki forced to go commando. Takeda trying to talk to her. Dramatic Wind kicking her skirt up. Hilarity Ensues. Particularly due to how Mai reacts to it - the scene cuts to Mai in the bathroom shortly after, laughing her butt off at the memory, even saying she's going to Die Laughing!
After Natsuki announces that she won't go after Mai and Mikoto anymore, seeing as they're already at Fuka and she has other concerns, Mai tells Mikoto no more picking fights. When Mikoto seems reluctant to agree, Mai threatens to stop cooking for Mikoto. Mikoto is suddenly very compliant.
Natsuki tracks Nagi down in the library to ask him for information. Nagi makes a comment about her catching a breeze on her "cute little bum". Natsuki shoots him with an ice bullet, leaving him dangling over the railing, denying he knew anything about what happened to her.
Episode 9
Natsuki has the misfortune of running into Takeda at the beach just as she's about to slip out of her rider suit and into her spy bikini. Then Takeda slips off the rock he was perched on, landing on Natsuki, whose scream draws Mai, who thinks Takeda and Natsuki are being intimate and runs off, apologizing for interrupting. Natsuki then proceeds to beat Takeda unconscious with his own shinai.
When Natsuki is forced to Show Some Leg to flag down a passing car, and the passengers turn out to be people they know. Reito can barely suppress his laughter, and Shizuru notes that it's "worth it" to see Natsuki like that. Shizuru's reaction either becomes rip-roaringly hilarious or heart-wrenchingly sad when watching it after knowing what happens in her Psycho Lesbian phase.
The sound dramas taking place after Episode 10, in which Mai, Natsuki, Aoi, Chie, and Nao get drunk, resulting in them talking about personal secrets, Natsuki and Nao actually getting along, and everyone trying to eat Mikoto. Nagi helpfully informing the viewer that you should only drink when you're 20 is also quite amusing.
The part in Yukariko's special when she fantasizes about men.
Yukariko: Sometimes, I think about it too, if I was brought up in an ordinary environment and met a boy m-my age just like all girls do and fell in love and was held in his arms and OHHHHHHH! (pause) Oh-oh my! What am I doing? Oh, Lord, please forgive me for having such a lewd and vulgar imagination!
In a meta example, Nagi sings off-key. This is an allusion to his voice actor's reputation as a bad singer which caused him to never do another Image Song after being ridiculed. It's a wonder how he was okay with this scene.
During the "Cake baking contest", the cake that Haruka, Shizuru, and Yukino were baking (honestly, mostly the efforts of Haruka and Yukino) falls on the ground. Shizuru of all people invokes the Five-Second Rule.
Earlier, Haruka makes the mistake of heating chocolate on direct heat instead of using a double boiler. When boiling chocolate flies out of the pot, Shizuru nimbly dodged it with a simple tilt of her head.
At one point, Yukariko suggests to Nao and Natsuki "Let us pray." They do.
When confronting the Orphan, Natsuki seems particularly offended, "Do you know how hard we worked on that cake?!"
During the Karaoke party, there are a few things to amuse.
Natsuki is selected by a spinning wheel to sing first. Under protest she is dragged behind a curtain and forced into a girlish pink dress that doesn't suit her at all, complete with Girlish Pigtails and ribbons. She has Cross-Popping Veins as Nao laughs at her, and proves herself Hollywood Tone-Deaf.
Nao stops laughing when her turn comes up, and Natsuki starts. In fact, she helps drag Nao into the changing area where she's forced into Age-Inappropriate Dress more fitting of a Vegas showgirl or Brazilian carnival. Natsuki's laugh is accentuated by her slapping the sofa in hysterics.
Mikoto seems unphased being put in a frilly swan outfit.
Midori, having had a few too many, goes into Alcohol-Induced Bisexuality and tries to strip a protesting Natsuki while leering at her like a Dirty Old Man. Yukariko, similarly soused, tries to kiss Nao.
Natsuki and Nao, who have plenty of vitriol and none of the best buds, are collapsed against each other in costume from exhaustion.
Mai, who loves karaoke, keeps hoping she'll be selected, is frequently disappointed, from the wheel seemingly selecting her,only to move a space at the last second, to a button flying off of Midori's vest and hitting the wheel, shifting the selection again.
In the Finale, as the resurrected Hime speed towards the star to destroy it, Natsuki demonstrates that she's Not So Above It All by stealing Midori's thunder.
In the finale, it looks like Mikoto has made a fatalHeel–Face Turn...until her stomach rumbles and Mai flips her over to reveal Mikoto alive and well with Wingding Eyes. She laments, "Mai, I'm starving. I'm a goner." All of the other HiME stare in disbelief, save Natsuki who delivers a very dry "What?".
Manga
Haruka's Lotus-Eater Machine dream, which shows what the world would be like if everything went her way. She holds multiple positions of great power and influence and has an entire harem of naked women in her bath, which potentially says much about her true sexuality.
