In Azumanga Daioh, Yukari occasionally brings up a Love Letter incident involving Minamo from when they were in High School, which usually prompts Minamo to scramble to get her to shut up. Once, she sang "love letter" (In English) whilst flitting down the hallway, just before Minamo could relate a juicy detail about Yukari to the students. Watch the anime version of the scene, as it must be heard to be appreciated.
Another Noodle Incident (at least from Minamo's point of view) happens during a Beach Episode when she gets drunk and answers all the girls' questions about sex. In the morning, Minamo wakes up with a hangover and no memory of the previous night; then 11-year-old Chiyo asks her to clarify a few points... While she's digesting that, the other girls show up to formally thank her for the very educational lesson.
The Pokémon anime's Lovable Sex Maniac Brock, during the Orange Islands sub-arc, seems to legitimately settle down with the Island's female Pokémon Professor, actually leaving the group for a while to pursue the relationship. When he returns, it's clear that something happened to turn the relationship sour, but he refuses to elaborate, instead going into a deep, brooding, Blue with Shock depression whenever anyone even mentions the relationship or the Professor's name.
In the D.Gray-Man manga, almost nothing concerning Allen's time with Cross is outright shown or explained; Allen gets too traumatized remembering.
Allen once recalls an incident involving his mentor Cross Marian's stash of alcohol-filled chocolates. What happened after he ate them is never explained explicitly, but the incident pissed Cross off enough that he punished Allen big-time and forced him to promise to never touch a drop of booze again. In the "Kuro no Bansankai" Special Drama CD, however, we find out how Allen behaves when drunk: he gets VERY vicious and destructive, and when it wears off, can't even remember he was the one who caused all the massive property damage. As a result, Lavi is able to take a very, very good guess as to why Cross banned him from ever touching alcohol again.
When he was playing cards against Tyki and his friends, he mentions he had to gamble (and therefore cheat) to survive, and off to the side, we see something saying "a typical day", where we see only dialogue talking about Cross owing money....
Kallen: This reminds me of Aomori. C.C.: It isn't as bad as that was. At least everyone here is wearing their clothes.
An image released with a special edition DVD for the end of the series depicts C.C., Kallen, and another soldier running from searchlights while wearing nothing but towels, explaining this incident and rendering it no longer noodle.
Also, in the final episode, Nina asks what happened between Lloyd and Rakshata. Cecille just said it was "such a minor thing."
Played with in the Cromartie High School anime: the rather upstanding Kamiyama refused to explain exactly why in the hell he's in a school full of Japanese Delinquents. However, he tells the audience several times that if they want to know they should read the manga (in which it actually is explained).
In Tsukihime's side-story game, Kagetsu Tohya, Shiki occasionally refers to the haunted house his class did last year, in which he and his friend were responsible for something that resulted in their student government making an amendment that strictly prohibits tea kettle monsters, mushroom monsters, and any pot that uses the aforementioned things. The specifics are left up to the imagination.
Shiki: Yes, we did a haunted house my freshman year, too. Well, Arihiko did his part so ardently that we were forced to stop in the morning. (To himself):The Inuidake Children Kidnapping. It's an event that will forever remain in the annals of the student government.
Lina Inverse in The Slayers references the horrible punishments her sister Luna used to put her through quite a few times, even though they are never actually explained. It leads one to wonder what she really could do, granted that Lina could put up with being electrically shocked while saying it was nothing compared to that torture. That, and Lina constructed a pyramid atop herself in order to merely get away from a letter sent by Luna and just the mere reference to her causes Lina to fly into a mortal panic.
One of the less harsh punishments Lina suffered involved a whole lot of slugs, a fact which she tearfully reveals after a near-total fear-induced breakdown in the second season.
An unspoken Noodle Incident is whatever it was that caused Naga the Serpent, Lina's self-proclaimed rival (and whom Lina publicly called "Goldfish Poop" in the novels, due to her habit of following Lina), to stop following Lina by the time the anime started.
In the Mai-Otome anime, Shizuru and Youko recall a mishap that occurred during Natsuki and Mai's attempt at the survival exam. Shizuru notes that when she heard Natsuki's distress signal, she rushed to the scene as quickly as she could, only to find the two girls in a "most improper" position, at which point Natsuki angrily cuts her off and tells her to "forget about it" before she gets to the juicy parts.
In chapter 46 of Katekyo Hitman Reborn!, Tsuna visits Longchamp's house. While there, Longchamp is attacked by a girl named Pantera (although he assures Tsuna that she's aiming for him, but has really bad aim). When Tsuna realizes this, he asks if something happened between the two of them, and Longchamp's Number 2 guy assures him that nothing happened and not to ask him about it again. Tsuna takes this as proof that something happened. Read the page here.
It has been mentioned that Aya has had many unusual exploits as student body president in Fruits Basket. One specific one apparently involved the Dean of the school's statue.
Hatori would often threaten to reveal Shigure's many incidents if he kept making an ass of himself (or those around him).
Edaniel has his own letter column on the Bizenghast website. In one letter he mentions that he once dated a human agent, who he later broke up with at the Mausoleums request. Why the Mausoleum wanted them to break up is never mentioned.
In Get Backers, the reason for Takuma Fudou'sstalker obsession with Ban is vaguely explained by Ban to have started from Ban ripping Fudou's arm off during an incident in the past. It's never elaborated on (other than that it happened while Fudou was working as a raider). However, knowing Ban's arrogant, condescending attitude, along with Fudou's Ax-Crazy, depraved ways... it's not hard to guess the reason why it happened.
Averted just to be played straight in Love Hina. After Motoko runs away from the Hinata House, we learn from her big sister that her hatred for men comes from a time when she caught them kissing. But she puts it as "since then, Motoko started to loathe men and turtles". One wonders what the poor turtles have to do with it, like Keitaro wondered.
In Lucky Star there are several scenes that begin with one character finishing a conversation talking about how something stinks. It's a bit of a running gag, but after seeing it mentioned two or three times it makes you wonder what smells so bad.
In Fairy Tail, part of the S-class Mage test for the guild had Lisanna and Juvia failing to get past Erza, which just seems like something that wasn't elaborated on for the sake of time. But then if you look closely, it becomes a Noodle Incident as to exactly how Lisanna lost her pants.
There's occasionally reference to an incident where Izaya framed Shizuo for a crime. What crime that might be has never been elaborated upon.
To say nothing about their high school days. Shinra was apparently doing a lot of damage control:
Shinra: Other things happened too when I was in school. There was this "The Pool of Hell Opens - Chlorine Gas Everywhere!" incident, "Real Flesh Art in the Art Room" incident, "Cultural Festival Campfire Explosion" incident and of course "Field Trip to the Shambles - the Okinawa Arc"...during the three years when we were in Raijin, gasoline drums were rolled down from school buildings as part of the routine. Really, it's hard to believe how nice and orderly this school has become these days...
Also, during Shinra's -first official?- date with Celty he threathened Izaya, who had been stabbed and was bored at the hospital if he kept interrupting his date.
Shinra: Oy Izaya! If you don't cut the heck out, I'll start telling people about that thing back in middle school!
The last one is a special mention because Izaya is the type of person who would ignore a threat like that. However, this threat in particular shuts him up.