Obviously, no-one knows what the original Noodle Incident involved.
The earliest reference to it, perhaps, was when Calvin's mom goes to a parent-teacher conference, and Calvin is dreading her return. When she gets home she catches him packing, which prompts him to immediately protest that everything was a lie, at one point bringing up "the noodles," which his mother had not heard of yet.
Calvin: She told you about the noodles, right? It wasn't me! Nobody saw me! I was framed! I wouldn't do anything like that! I'm innocent, I tell you!
Mom: What noodles?
Calvin: Oh... Uh... Ha ha! Did I say noodles? You must have heard wrong. I didn't say noodles.
In one strip, Calvin complains to Hobbes about how much trouble he got into that day in school, but when Hobbes asked what happened, Calvin says he doesn't even want to talk about. When Hobbes asks if it had "anything to do with those sirens [he] heard around noon," Calvin repeats, louder this time, "I SAID I don't want to talk about it!" In the strip that immediately preceded this one, Calvin is getting dressed for school, complaining about how it never changes, and then says, "Well, not today. Today, I go for the gusto." and puts on a cape and space helmet, which seems to suggest the obvious. Moderate consensus among fans is that this is indeed the specific date/strip that the Noodle Incident occurred, as no other school exploit of his ever got all the way up to the level of emergency sirens.
Another possibility involves a story where Calvin does an oral report on the human brain, and brings a bag of cooked noodles as a visual aid.
Half the fun of the Noodle Incident is watching how flustered and angry Calvin gets whenever Hobbes brings it up... Yet whenever anyone else brings it up, he goes into a defensive panic attack and claims he was framed.
According a later Christmas strip, even Santa Claus doesn't know exactly what happened, or whether or not Calvin is innocent, despite having magical surveillance systems. He probably knows the broad outline, of course, since it's not that people don't know the details in-universe.
Bill Watterson may, at one point, had intended to visit the Noodle Incident someday, but in the Tenth Anniversary Calvin and Hobbes collection, he explains that the reason he never did was because nothing he could come up with would ever be as fantastic or as interesting as anything the readers would be able to come up with while trying to work out exactly what happened.
Hobbes: What about your explanation of the noodle incident?
Calvin: That wasn't a story! That was the unvarnished truth!
Hobbes: Oh, don't be so modest. You deserved a Pulitzer.
A "Salamander Incident" was referenced in an earlier strip.
We the readers were also never privy to Calvin's favorite bedtime story Hamster Huey and the Gooey Kablooey. At times, Calvin's dad gets irritated with the actual story and begins to ad-lib; in one such ad-lib, Calvin wonders at the end whether the townspeople find Hamster Huey's head (come to think of it, this brings up the question of whether or not a severed head is involved in the original story as well).
The only hints revealed of what was in the book, is that there is a dance called the "Happy Hamster Hop", and that reading it aloud requires "squeaky voices and gooshy sound effects".
Mom: But you look cute doing the Happy Hamster Hop.
Dad: I don't WANT to look cute!
In one strip, Calvin says that the book's author (Mabel Syrup) has written a sequel to it called Commander Coriander Salamander and 'er Singlehander Bellylander. His dad's reaction to this news?
Dad: Architects should be forced to live in the buildings they design, and children's book authors should be forced to read their stories aloud every single night of their rotten lives...
Calvin's show and tell from this◊ strip...if he even had a show and tell.
Calvin: Today for "show and tell," I refuse to show you what I brought and I refuse to tell you anything about it. It's a mystery that will haunt you all your miserable lives! You'll never, ever know what I brought! You can beg and plead, but I'll never end your torment! I'll carry my secret to the grave! It's the show and tell that was never shown or told! Ha ha ha! Ah ha ha ha ha!
(Cut to Calvin walking to the principal's office)
Calvin: Everybody wants the same old thing.
In one strip, Calvin's parents receive a phone call from a neighbour that Calvin is running in her yard naked and tied to Hobbes (which is actually explained in the strip itself), and Dad asks Mom to handle it, as he was the one who "got the little nudist out of her bird bath".
There's a substitute teacher who appears only in one strip and is referenced only in three. She's introduced in the middle one, and in the last one, Calvin is home and mentions that she left at noon.
In one strip, Calvin and his mom come back from a children's matinee movie. He had barely noticed there was a movie on, and she looks messy and extremely tired (and demands they purchase a video player when asked how it went by her husband). Obviously he found something else to do.
In one strip, Calvin asks Hobbes a "hypothetical" question about whether he should tell Dad if he's done something bad. Involving his car. Which could perhaps be repaired if it could be found first...
Later, there was an otherwise unrelated Story Arc in which Calvin was shown accidentally pushing the car into the ditch across the street, and even though there was no damage this time, Calvin's reaction makes it clear he was expecting a repeat of the time it was both lost and in need of repairs.
Calvin once calls his dad to pick up topsoil and grass seed on his way home from work. Dad, being busy, brushes it off with "OK, sure. Goodbye." We then see Calvin walking away from the phone covered in dirt and carrying a big shovel, and Calvin's dad looking very puzzled.
During a visit to the natural history museum, Calvin's parents remark that they haven't been there in a while "at the museum's request" and ask Calvin not to bite anyone this time (though considering the exhibit in question was dinosaur fossils, we get a pretty good picture on this one).
In another incident, Calvin put worms on his dad's dinner plate. Like the Trope Namer, he doesn't want to talk about it, and it seems to be a Never Live It Down moment for him.
Another strip has Calvin asks his dad "Would you still love me if I did something bad? He means something "really, really" bad. Dad asks "CALVIN, WHAT HAVE YOU DONE?"
Calvin's parents are once shown discussing child rearing after "the contractor says it will cost $200 to fix". It's never mentioned what exactly Calvin broke.
One strip shows that Calvin flooded the house. How he did this is never touched upon.
Another strip, he's worried about his dad finding out his broke his dad's binoculars. When Hobbes suggests that maybe Calvin could repair the binoculars, Calvin goes gets the binoculars. He brings a box and tells him "don't sneeze" as he pours out a pile of very tiny pieces. How he managed to do that to a pair of binoculars, is never elaborated.
A literal noodle incident happens in FoxTrot, and as a result Jason gets all of his Calvin and Hobbes collections confiscated.
In Get Fuzzy, the purported reason that the veterinarian doesn't make calls to the Wilco house is "the Hockey Stick" incident, for which Bucky is responsible.
A few other "incidents", like the Bag War, are expanded into full story arcs as extras for the back issue collections.
In the popular comic strip Pearls Before Swine, Pig is enemies with a sea anemone due to an unknown event that occurred years in the past. It's a Feghoot for "Annie-May, my anemone enemy".
A Bloom County strip had the middle two panels interrupted for an "editors note," leaving only the first and last panels free. In the first panel, Portnoy is asking Opus if he's heard the latest news: the last panel had Opus yelling "Turnips! Turnips and Antifreeze!" while Portnoy was yelling back "Not with Donny Osmond he won't!"
Garfield's owner Jon has tons of these, and he's certain to bring one up every time he opens one of his yearbooks, or family albums, or simply talks about his past. (The scary thing is, as goofy as Jon is, he seems to have an extended family full of relatives who are goofier.)
The whole "Thompson is in Trouble" Story Arc from Peanuts was one Noodle Incident after another. It started with Snoopy getting a coded message from the Head Beagle saying that "Thompson is in trouble", with Snoopy recognizing the name instantly and remembering a past incident with "that stupid Thompson" that "almost got us all killed". (It's only confirmed later that Thompson is another beagle, but one can only guess what happened the last time, although Snoopy complains through the whole story that Thompson would "never listen to advice" and other such faults.) Snoopy leaves quickly to find this Thompson, does some investigating, questions a waitress in a restaurant "full of shady types" (who remembers Thompson), gets lost in the rain, and finds Thompson, but he's too late. The readers find out in the next strip where Snoopy writes his report to the Head Beagle that he had witnessed Thompson try to deal with ten-thousand rabbits by himself, and was presumably killed. (Again, it is not revealed why.) In the last strip of the arc Charlie Brown asks Snoopy if he thinks he'll ever know what happened, and all Snoopy can say is that "Those rabbits gave him an offer he couldn't refuse!"