Chapter 9 of the manga, a dialogueless attempt by Mio and Yuuko to build a house of cards that predictably ends in disaster. Mio weeps as if someone died.
Episode 17 of the anime adds orchestral music and Nano threatening to push over the cards with sleepy nose bubble.
In Episode 1, Nano accidentally runs into a boy while running. This would easily fall under Meet Cute... had it not been for the spectacular explosion that resulted from it. Bonus points for the slow-motion shots of Nano's sandal falling to the ground and a petal landing on her head just before the explosion.
The students are standing outside for announcements (or something of that nature), when Sakurai-sensei asks the students which one of them put a Maitreya Buddha carving in her locker (most likely Mai). When the principal stands up and says it was him, you see a couple frames of Takasaki-sensei bursting into flames. It only lasts a split-second, and it will be much later in the show until you can understand the joke upon rewatching it, but it's worth it. The look on his face is priceless.
Nano's dilemma with the cockroach under the bowl. The way she processes the situation in her thoughts is so much like your average action anime scene, with all the drama of having to disarm a bomb. It only gets funnier once Sakamoto shows up.
Sakamoto: How am I supposed to get it if you don't lift the bowl?
Nano: Lift it yourself!
Sakamoto: How am I supposed to do that?!
The camping trip. ALL OF IT. It's basically a conga line of bad stuff happening to the girls, made even worse for them by Mai's pranks.
For that matter, any time Mai pranks Yuuko is seriously hilarious. Episode 4 is particularly epic in this respect.
Sakamoto's first words, and the events leading up to them.
Episode 5's Helvectica Standard: Projectile Toast that launches with enough speed and force to punch a hole in the roof and kill an unsuspecting mouse.
Any time Yuuko thinks she's doing something right, only for it to backfire immediately, and her off-the-wall reactions to it. Happens Once an Episode at least!
Episode 9: After surviving a test together, two friends cry tears of joy, another student tells everyone they are getting a free bag of rice, and two students announce they are getting married.
The epic way Yuuko tries to kill the mosquitoes that bother her in her sleep.
Speaking of mosquitoes, Nano is also bothered by one inThe Stinger. She slaps her hands in a feeble attempt to try and kill it, and when she realizes she did, she is so horrified she faints and falls on her screw.
Episode 10: Annaka goes to a nagashi somen event, only to find that it's a cheap imitation of the real thing. Endless "EEEEEEEEEEEEEEEEEEEEEHHHHHHHHHH??" ensues.
Episode 11: The vice-principal notices that he doesn't have any more string or straw to make a doll to put in the principal's shoe locker. This reminds him or other bad things that happened to him recently, which reminds him of other bad things that happened to him recently and in his life (for example, the only thing he got for his birthday is a butter roll). The guy's life sucks so hard it's hard not to feel sorry for him, but you can't help but laugh either. It gets worse for him when his daughter and grandson visit him. He gets a Hope Spot, thinking that playing with his grandson will help him feel better, but while the former goes to make dinner, the latter gives his grandpa "chocolate" buns, actually made out of mud, and insists he eats them. Not wanting to sadden his grandson, the vice-principal eats the mud balls, and collapses.
Yuuko just got better from a cold, but realizes that her final exams are the next day. Of course, she didn't study anything, so she tries to spend the night studying at least English. Unfortunately, she gets lost in her thoughts, and ends up writing a poem instead. Twice.
Episode 13 has a scene where Yuuko insists on showing Mio some magic tricks, but she's too sick to stand on her own two feet, let alone realize she keeps losing her props; as Mio is trying to pretend she didn't see anything, it makes her more and more uncomfortable. By the end, Yuuko has outright passed out. Mio puts the flowering wand by her desk, as if she had passed away rather than out.
Mio goes berserk when her Covert Pervert drawings get exposed and in the process of trying to collect them all attacks a cop, Yuuko, Oh Gentleman, and Sasahara's goat.
The build-up to that moment is also funny: When Mio realizes that she coincidentally has the same kind of bag as a criminal the cop is after, she gets nervous and keeps acting more and more suspicious. Yuuko's over-the-top reactions are hilarious. At one point, Mio even puts her hands forward as if she was turning herself in, and Yuuko tries to cover for her by saying that she's just preparing in case a stray volleyball comes her way.
Episode 17: Nakamura-sensei's Pit Trap gets Nakanojou instead of the desired Nano. What does she do? Pull out an electric trimmer and shave off his mohawk.
Mai's trolling gets so out of hand, Yuuko unleashes a Skyward Scream so loud that most of the population hears it. This includes the school gym, Sakamoto back at the lab, a mugger holding his victim at gunpoint, said victim, and some dude living in the sewers.
Episode 18: Yuuko is playing one of those crane games. She has the toy firmly grasped in the claw and proceeds to bring it up... only for the claw to suddenly break off mid-ascension. Her face right afterwards is priceless.
Yuuko is riding the train to a neighboring town to get to a Daiku Burger restaurant where she was supposed to meet with Mai. However, she keeps embarrassing herself, causing a little girl (a certain Tsundere's little sister, to be exact) to keep laughing at her. She eventually takes Yuuko to the DB, where she meets up with Mai, dressed in a full medieval armor. Believing it was Halloween, Yuuko grabs a pair of funny glasses and fake nose from her bag, puts them on, and says "Trick or treat". Misato then remarks how Halloween ended a week ago, while her sister is laughing so hard she's banging on the table.
In a random and surprisingly beautiful segment from "Helvetica Standard", a young woman is trying to get to an old library to find a book that she had read in her childhood. She eventually finds that book, and sits down to read it. She opens it... and finds a gun inside.
Episode 19: Mio attempting to jump over a pole. After a long Inner Monologue you're expecting a Crowning Moment Of Awesome...instead, she jumps and nails Yuuko in the stomach with a headbutt. Yuuko tackles her as well so she lands on the mat.
Episode 20: Yukko helps Mio with her manga, and grabs a mechanical pencil. She tries to click it... from the wrong end. Her scream explodes through the house, out into space and blasts through all of the planets (and Pluto).
Mai's trolling and Yuuko's failed attempts to repair a huge mistake she made after spilling her ink on her page as well. Eventually, Mio goes absolutely nuts and unleashes a huge rant about how Yuuko kept trolling her after she told her to buy some paper. Turns out she unknowingly made most of that stuff up from the frustration, and Yuuko actually did buy paper.
Episode 22: What Nano wants as Christmas presents.
Yukko and Mio get bitten by Mai's two dogs, causing them to scream so loud that they fire Wave Motion Gunsfrom their mouths that pierce the heavens along with several buildings.
Episode 23: Sakurai-sensei finds her brother's porn magazine. Hilarity Ensues.
The Helvetica Standard from Episode 24: A girl convinces her friend to tell her the name of the boy she likes, promising one million yen if she reveals the secret. Immediately after being told, the girl tells the entire class and then plops down a stack of bills on her friend's desk.
Episode 25: Nakamura-sensei discovers the Shinonome Lab. Her paranoia promptly runs amok.
Episode 26: Nakamura's cat, Taisho a.k.a Sakamoto, remembering the horrible conditions she unknowingly caused him, including trying to feed him noodles, and spilling said noodles on him, and trying to give him a bath like a child. Even better when Sakamoto thinks about how his living at the lab is not much better since he has to constantly put up with Professor's pranks and comes to the conclusion that his life sucks no matter where he goes.
On the fan-made side of things, this video features the second opening of the anime set to the theme for Game of Thrones. In the poster's own words: "This shouldn't work."
This scene, where Yuuko and Mio try to break a pumpkin open. The catch is that this pumpkin seems to be made of titanium or something, as it just won't even get a scratch, no matter how hard the girls hit it.
Even better since it quickly goes from normal things, like smacking it with a stick, to over-the-top shounen-manga-style super-attacks.
The girls have just finished eating their meal in a restaurant. They see Mai folding her napkin into a chopstick stand and follow her. Unfortunately, while Mio and Mai make pretty good stands, Yuuko has her face completely down in shame: she didn't fail in making a chopstick stand, but she misunderstood what Mai was doing, and made a crane origami. A very small one, in fact.
Overlapping with Awesome Moment, in manga chapter 143 Mai engages in troll-on-troll combat with Mio's older sister.