Shermie vs. Bryan's special intro in KOF'98 Ultimate Match. He keeps shouting "WOO! WOO!". This annoys her so she walks over and SLAPS THE TASTE OUT OF HIS MOUTH.
Billy's special opening against Iori is understandable, given what happened at the end of '95. What's less expected is Eiji Kisaragi teleporting in to shake his fist at Iori and then teleporting away before he's spotted.
Yashiro would rib on someone who's got business with the Orochi bloodline outside his own team, by using Chris' "Oh no... he looks strong..." (and ending with "...NOT!"). So how was this funny? Well, switch him to the more monstrous Orochi Yashiro, and he'll do the same while still in the crueler form (the same intro is used in KOF 2002 and its Unlimited Match release, albeit with Yashiro saying Shermie's "I won't like it if it hurts..." (and still ending with "...NOT!")).
The Art of Fighting team's ending in KOF XI: Ryo and King are in a fancy restaurant waiting for Yuri. When the waiter shows up, it turns out to be Yuri in disguise, a fact Ryo and King notice immediately. A second waiter shows up, and it turns out to be Robert. It is at this point we actually see the ridiculous disguises they're wearing. At which point Takuma shows up, dressed as the manager (and wearing the Mr. Karate mask as his disguise), and offers them a key to the penthouse. King promptly throws a fit.
Having Team Kim fight against Team Yagami in KOF XIII Story Mode, in which Kim tried inviting Iori to join his Tae Kwon Do dojo, and even prepared a taekwondo gi just for him. And if not enough, he also invited Hwa Jai and Raiden to the sport as well (He offers the Chang-sized gi for Raiden). Hilarity at its finest.
Vanessa: This is Vanessa. I'm investigating the area around the stadium...but there's too much ground to cover. I haven't found anything. I need something specific to go on. I can't just search an area this big for anything "out of the ordinary." I feel like a lost tourist.
Mary: This is Mary. I'm in the slums, dealing with an...unsavory individual. (Screenshot reveals this to be Duck King) I haven't come across anything of note.
XIII Team Fatal Fury Arcade End: During the victory celebration, both the Bogard Brothers are congratulated by Mai (who embraces Andy) followed by Mary with Anton (who approach Terry). As Joe takes note of both of them being fawned over by girls, much to his jealousy, he is seemingly embraced by a woman from out of nowhere. He cheers initially until he asks her who 'she' is only to discover it to be the same transgender man he saved in 2003 who is unfortunately looks nothing like a woman with the stubble, despite the makeup. Cue horrified Joe trying to run off, got caught and end up looking like he's Deader Than Dead...
The Art of Fighting Team ending has Yuri being asked by an interviewer about what would be the ideal husband. Behind her, Robert is holding a ring box, working up the nerve to ask for her hand in marriage. Takuma notices this and stomps Robert's foot before he can say anything. Robert responds in kind and they go on stepping on each other for the rest of the scene. Meanwhile, Yuri is trying to pair up King with her brother Ryo, who seems oblivious to both this and the squabbling behind them.
Chin and/or Kim get Kyo all pissed off via asking him if he actually did finish higschool or not;
It's even funnier if the player chooses Team Japan for Story Mode and finds the Psycho Soldiers. Athena naively asks Kyo if he did graduate or not when he asks about her uniform, Kyo is at a loss of words despite Benimaru telling him it's fine, Kensou is all "WTF?!"...
While the first is removed in XIII Climax, the latter is even funnier. In the original, when Athena asks why would he keep such data, Maxima calmly says he's just interested in her Action Girl strength. In the new version, it becomes a Suspiciously Specific Denial in which Maxima totally didn't store pictures of her for non-fighting purposes. (Hint: yes, hedid.)
However, the first quote is revised for Climax with Maxima saying that Kensou "turned the output of his mouth up to 11".
King asks Andy to pay for Terry and Ryo's tab at her bar, which makes Andy really damn angry.
Team Kim's ending: Kim's not so subtle attempts to ditch his master Gang Il and his master's girlfriend Luong are hilarious, even more so since it ends up having the opposite effect with the two deciding to remain at Kim's side for an indefinite period of time.
Team Mexico's ending: King of Dinosaurs debates with himself over what diet would be best for developing muscle as well as fitting his image as a dinosaur/role model for children, while a remix of Yuri's "Diet" from Art of Fighting 2 plays. He also admits that he skips leg day every now and then. Angel and Ramon then enter and begin petting King of Dinosaurs as if he were an overgrown puppy. For bonus points, King of Dinosaurs and Angel purr. Ramon even develops a new technique he names "Tiger Petting", which proves too vigorous for Dinosaur, who then roars and attempts to bite Ramon's head.
The special opening between King of Dinosaurs and Mian, where he mistakes her for "an assassin from ancient times to extinguish the dinosaurs" due to her Bian Lian mask. She is completely confused and concludes that he is simply an idiot...into which he doesn't take well.
The special opening between Terry and King of Dinosaurs. Let's just say they both suck at kayfabe.
Luong and Kim's special intro. Luong's innuendo laced dialog makes Kim feel very uncomfortable. Kim has to cut the conversation short by reminding Luong he has a wife and two children.
Newcomer Kukri spends most of his time trolling every other character in the game.
A small moment in Team Japan's ending where Kyo and Benimaru are flabbergasted that Daimon decided to wear Antonov's crazy looking championship belt.
Team Women Fighters ending, again. The girls are celebrating their victory at the Pao Pao Cafe, with other non-evil female characters from different teams as well as former Women Fighters members like Yuri and Blue Mary joining them in celebration. King then tells Richard Meyer that she should get her food and drink on the house for winning the tournament, then the rest of the women hear "on the house" and start ordering more stuff. At this point he panics and asks Bob Wilson to call in Terry, Andy, and Ryo because he's worried that if he tries to stop this on his own, his bar will be wrecked. Once the boys arrive, however, the ladies are quick to tell them that the house is "generously" comping everyone tonight, which naturally leads to them placing huge orders and Kasumi and Ryo declaring an eating contest. Desperate to save the bar from financial ruin, Richard concludes that at a time like this, he mustuse Haoh Sho Ko Ken... only he can't, since that is a high-level Kyokugenryu technique.
Andy and Mai's special intro starts with Mai asking if Andy turned off the AC before they left. He didn't even touch it, which makes Mai fret, and want to hurry the fight along so she can look into it. Andy suggests that she'll be too distracted to fight at full force.
Yuri's command throw against Chang. Normally she delivers a series of Armor Piercing Slaps to the enemy's face, but due to Chang's huge size difference, she repeatedly slaps his man-boobs.
Zarina meets Nakoruru and introduced her to her toucan Coco, which is friendly. Then Nakoruru starts describing that her Mamahaha have been eating hamsters because it's a carnivorous bird and its favorite food is rats (hamsters are just substitutes). Zarina then freaks out while telling her Coco to escape.
Antonov's climax super, if it connects, has him spit out his cigar and perform a mighty suplex on the opponent, strong enough to plant them into the ground. The camera then immediately smash cuts to him standing, an extreme close-up of his championship belt, which is revealed to be a cigar case. He pulls out a spare cigar, lights it, and continues fighting.
King freaking out when Ryo asks her to come over with him.
Ryo: If I win I'm gonna take you on as a student, whether you like it or not.
King: I'll give it some thought, Mr.Sakazaki.
The special opening between Meitenkun and Vice. As Meitenkun sleeps, Vice attempts to wake him up by telling him that the match is about to start. She succeeds...only for him to fall asleep again...prompting her to kill him instead.
Meitenkun: Zzzzz... (snoring)
Vice: ...Yo, brat. The match is starting. You gonna wake up soon?
Vice: Finally awake now? Alright, let's go ahead and start.