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The Opening to Overman King Gainer which includes several of the cast and robots doing the monkey. It also includes Gainer, and Sara first dancing in the forest before doing figure skating.
In the series itself Gainer announces his love for Sara which causes Sara to storm off blushing. This would have merely been embarrassing, but Gainer did it while an enemy was using an Overskill to broadcast everyone's thoughts to everyone—thus, everyone heard it, and quite a few of them shouted encouraging things at Sara whilst she stormed off blushing.
Sentou Mecha Xabungle had at least 4 of these per episode, be it physical, a pun, or just something coming in from left field—it delivered the funny.
But the crowning point would have to be—after Jiron, whose head is very round, has been called "DO-Manjuu" ("Big"; Manjuu is a kind of round confection) for most of the series—when Jiron Amos is finally decried as MELON Amos. In Jiron's reaction shot, his face is briefly a melon. Must be seen to be believed.
Alpha Gaiden includes that instance. This image has not been altered◊. The fan translation gives this scene a Pragmatic Adaptation to keep the joke; Jiron is called "Melonhead" by one of the villains, and after getting fed up with it, causes the villain to instead call him "Melon" Amos. The two words sound very similar in Japanese.
That, and the infamous Missile Toss, in which they catch a giant missile with a Mecha maybe a fifth the weapon's size, then throw it back.
Hyakko is already pretty random, but especially funny is the scene in which Nene and Torako (!) check out the students' uniforms. Nene is downright hilarious as a lecher who ogles every cute girl who walks through the gate. The way she "outs"herself and the reponse of Torako and her friends are also golden.
In Chrono Crusade, after Satella implies that Rosette can't dance, she drags Chrono onto the dance floor and tries to prove that she can. However, she can't, and Chrono is just as confused—the results is one of the best Slap-Slap-Kiss moments in the entire series (anime OR manga), absolutely hilarious AND a Crowning Moment of Heartwarming all at the same time. Definitely one of the most memorable scenes.
Episode 31 (manga): When the salesman decided to return to Matsuri's house in hopes that her mother would be home, the realization that all the "scary little girls" he had been encountering along the way (save possibly Ana) were already there, and he was about to encounter them again... Unfortunately, some of the humor is derived from his undeserved perception of being a pedophile, started by Miu's lie and seemingly substantiated by Matsuri's poor explanation skills.
Episode 3 (anime): Matsuri saying "nya" after every sentence is simultaneously funny and adorable, particularly when Ana calls, and when she demands the others nyaht follow:
Matsuri: Do you understand nya? I said, "Do you understand, nya?"!
Nobue:(enamored) I hear ya, nya.
Episode 12 (anime): The teacher in Ana and Matsuri's class picks on Sasazuka again and tells him to "go stand in the hall". Sasazuka defiantly says "No" and sends the teacher outside instead.
More than 20 years have passed and This Troper still laughs at the antics of the three micronized Zentraedi spies who arrive to the SDF-1 and have no idea of anything. Hilarity Ensues when they try to blend in.
This troper finds a certain scene in Episode 2 simply hilarious: A truck driver asking a Humongous Mecha.
(hooting) "Hey, buddy! How 'bout getting off the road?"
Macross Frontier has several ones but the one taking the cake is Ranka's pet Vajra Ai-kun tangling himself in Sheryl's panties while the latter is taking a shower... then running out of the room into the middle of a large group of Sheryl-crazed fanboys who were trying to listen in. As soon as an irate and towel-clad Sheryl screams after the little thief, all the boys realize the opportunity and a school-wide panty chase begins. Naturally, Sheryl responds by hijacking Luca's EX-Gear and joining the hunt while Going Commando.
Hi*sCoool! SeHa Girls: in the first episode, the heroines, trying to find out about Sehagaga Academy, find out about the school's song courtesy of Mega Drive. Alas, the school song is simply the old "Sega!" shout from the old Mega Drive commercials in Japan and the first Sonic the Hedgehog games.
Persona 4: The Animation, the King's Game. Everything about the scene is almost word-for-word the same as in the game...until Yu starts drinking...
Listing everything from Ninin Ga Shinobuden would take forever, especially if you have an odd sense of humor. In particular, just about anything Onsokumaru does could count. Or anything involving the ninja Redshirt Army. Or Shinobu. Or anyone really. Even the ending credits deserve a spot; where else are you going to see stop-motion, line-dancing ninja chasing around a flying smiley face with panties on its head while Japanese banjo-pop plays in the background?
Episode 16 of Cinderella Monogatari, Charles comes over to help Cinderella's stepfamily while Cinderella is sick. When Catherine sees Charles doing the chores, she tells him that if he marries Cinderella, she'll have them both hired to work at the castle—after she marries the prince. Of course, she (like Cinderella) are unaware that Charles is the prince.
Charles' failed attempt at cooking (complete with him wearing Cinderella's frilly pink apron) is also hilarious.
Episode 26 of Hunter × Hunter. One phrase: "IN OTHER WORDS, A PAPER TEST!". (Watch here, starts around 6:13).
One episode of Initial D has Itsuki riding with Takumi and demonstrating what he's learned about drifting. He attempts a drift... and stalls his car. He tries again, stalls again and cries, "ONE MORE TIME PLEASE!"
During a battle between Ryousuke and Kyouichi, Ryousuke makes a last-minute pass. As he makes his move...
In Episode 3 of Dai-Guard, Akagi claims that "I did not go crazy, I simply took an aggressive policy regarding my giant robot feet."
From Love Hina: In the English dub of Episode 5, Kaolla Suu's response to the telephone ringing. Keitarou is on the other end, calling from a train station.
Suu: "We're sorry, the number you have just dialled is not in service now!"
Two particular moments from To Love-Ru anime stand out. The first is Rito imagining himself taking part in taking part in intergalactic wars, with both scenarios ending with Zastin leaping forward whilst yelling "YOUR MAJESTY!" overdramatically. The second moment involved Lala using a magnet-like invention of hers to pull Rito to her location. The moment before however, Rito had been talking to Yui, but as the device activated, he ended up crashing forward and sweeping her into his arms, carrying her along with him. The two then crash through several locations each getting funnier than the last, starting with a mall, then a woman's clothing store, then someone's apartment, then a wedding, and straight into a funeral (where the (live) body burst out of it's coffin!), and finally climaxing in a war scene!
In the Japanese version: BAKABAKABAKABAKABAKABAKABAKA
Kure-Nai keeps the humor sharp yet suitably low-key through most of the series, exemplified by Benika's deadpan response to Renjou's outrage over her team's continued efforts to break Murasaki out of the Kuhoin compound: