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.
Despite some Unfortunate Implications, Golgo 13 has a rather notable one in the story "The Dark-Skinned Sniper". Duke Togo's target du jour is a corrupt politician in the Deep South. As part of a very intricate plan to get close to his target, Duke has taken a drug that darkens his skin color so that he can pass as black while staying with a cell of the Black Panthers organization (and catching up on his tanning). A group of cops raid the Panthers' shack, march everyone outside, and force them to strip at gunpoint so they can identify Golgo by his tanlines. Togo strips and stands up... and the cops glance at his crotch before mutually yelling, "Huh?!?" The other Panthers comment "Now he's a dark-skinned man all over! Do you see that!" "Kinda hard not to notice, actually." (For the record: The intimidated confused cops take them all in to the station, which gets Duke in range of his target.)
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 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: 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.
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 26 of Hunter × Hunter. One phrase: "IN OTHER WORDS, A PAPER TEST!". (Watch here, starts around 6:13.)
This Troper found most scenes with Eggman to be funny. My favorite though, is when he summons a robot for Sara to ride in. As she's thanking him for it, she gives him a big pat on the back, causing him to suddenly lurch forward and let out a painful "oof!" sound.
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 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:
Heroic Age has Age and the telekinetic twins throwing giant tubs of paint at each other in an early episode. Iolaous then walks in to find them and the cargo hold covered in paint: "Explain. Now."
In episode 16, when Mehitaka awakens on board of the Argonaut, the twins are there watching, screaming in terror and running around in utter panic (which looks absurdly adorable). Then they get a hold of themselves, prepare for epic ass kicking, fire a psionic attack... and fail. Utterly so.
In the second episode, Age jumps into the air, and lands on a table, eating all the food on it. Then he jumps from that table to another table. It's funnier than it sounds.
What makes this funny is that the crew of the Argonaut have prepared this amazing formal feast for the savior of humanity... and he turns out to be this wild, super-powerful, half naked boy with No Social Skills who just jumps around wolfing down food. While everyone runs around trying to stop Age, the captain just can't help but burst out laughing at the scene.
Age offers some fruit to Mehitaka. Mehitaka responds that his race doesn't eat anything living. The others ask what he eats, in that case, and he turns around, picks up a shovel, and consumes it whole. Age looks confused, picks up a shovel, bites it... and starts spitting in disgust. Then a few scenes later Iolaous is screaming at them to stop feeding Mehitaka pieces of his Humongous Mecha's armor.