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, aand 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.
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 once such incident, Calvin wonders at the end whether the townspeople find Hamster Huey's head, whereas we wonder what happened to Hamster Huey's head in the first place.
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!
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!
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. Obviously he found something else to do.
In one strip, Calvin asks Hobbes a "hypothetical" question 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 actually managing to sort of crash the car. It was much less spectacular than the untold version sounded to have been, and also seemed like it must have been the first time.)
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.
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.
During the incident in which Calvin breaks his dad's binoculars, he shows Hobbes that they've been reduced to powder. How this happened is never touched upon.
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.