In the Watergate tapes, President Richard Nixon repeatedly refers to a certain incident as "the whole Bay of Pigs thing." While it's never explained, he was probably talking about the disastrous Bay of Pigs Invasion in 1961.
Tampa Bay Lightning coach and former hockey player Guy Boucher has a very distinctive scar on his cheek◊. When asked how he received the scar, his answer was, "it's not hockey-related. I didn't tell anybody back home, so it's like this little enigma. My kids don't even know."
Similarly for the longest time Tina Fey would not reveal how she got the scar on her left cheek. She was slashed by a stranger as a 5 year old.
The creator of 7Up died without ever telling anyone how he came up with the name...
Apparently it has something to do with lithium, which has a mean atomic mass of approximately 7.
In LEGO's 2003-2004 promotional and story materials for "The Astrobot Diaries", in which two astronaut minifigures were chosen to go to Mars, it is repeatedly mentioned that Biff Starling is a replacement for another astronaut who suffered a "freak zucchini accident". When asked about this, characters respond with variations of either "It's classified/still being investigated" or "You don't want to know."
One of those "Reasons Why I Didn't Do My Homework" shirts you see being worn all over by juvenile delinquents in middle schools says "It was destroyed in a freak accident involving a hippo, a toaster, and a bag of frozen peas. You don't want to know the details"
Colbert: I want to thank you for not asking me about that thing that we pre-agreed that you wouldn't ask me about, ok? O'Reilly: Ok. The kid— the thing that happened... Colbert: Don't, eh-ah... ok?
When voice actress Amanda Winn Lee was asked in an interview to describe the scariest experience she'd ever had with a fan, she dropped dead silent for a moment before her husband Jaxon Lee suggested she talk about her second-scariest experience. See for yourself. She's never revisited the topic since.
Another voice acting related Noodle Incident: For years during The Nineties voice actor Tristan MacAvery was an employee of ADV Films and colleague of Matt Greenfield. Around the turn of the decade something happened between them that caused MacAvery to quit ADV and voice acting in general and develop an outspoken hatred of his former employers, Greenfield in particular. Rumors have been flying for ages, but this day only those involved know exactly what happened.
Marvel Studios and Terrence Howard were notoriously tight-lipped about Howard being replaced by Don Cheadle in Iron Man 2. It's still uncertain why Howard was fired, although money is an oft-cited (but not confirmed) reason.
In modern Turkey, the end of the Ottoman Empire during World War One is basically a big Noodle Incident that is taboo to talk about, mostly because that was when Turkey's Christian minorities began to suspiciously vanish.
The Creation of the Universe. We still don't know what exactly happened with 100% certainty.
The Roman poet Ovid did something that got him exiled to Tomis on the Black Sea by Augustus. Despite writing several volumes of poems complaining about his exile, he refuses to describe the cause more specifically than "a poem and a mistake" (carmen et error). Modern theories start with him being involved in Julia's love affair and move up from there.
For years, neither J. Michael Straczynski nor actor Michael O'Hare would say exactly why the latter was replaced with Bruce Boxleitner after the first season of Babylon 5. In June 2013, some nine months after O'Hare's death, Straczynski finally told the truth, having promised O'Hare that he would; O'Hare, throughout the first season, was battling near-crippling schizophrenia, but refused to seek treatment for fear of putting other people's jobs at risk and not finishing filming. Somehow he made it through the first season, to be replaced by Boxleitner for the remainder of the series' run. O'Hare asked JMS to keep quiet about it until after his (O'Hare's) passing, but asked that his story then be told in hopes of raising sympathy and awareness for those with mental illness.
On the Today show of May 27, 2013, Kathie Lee Gifford tells Hoda Kotb that she has been banned from returning to Santorini Island, Greece, and claims there is a big photo of her at the airport with the caption, "Do not admit." Kathie claims the reason why is because of a plumbing problem. When Hoda asks her what was the plumbing problem, she says, "I'll tell you at the commercial break."
In Terri Irwin's memoir of her married life with Steve Irwin, she recalls a family trip to Singapore where their young daughter Bindi decided to make tea while not wearing any pants.
Terri: When was the last time you had a girl with no pants fix you tea?
Steve: The last time I was in Singapore. note Steve hadn't visited Singapore since before he and Terri had met
Five decades later, Werner Herzog has yet to release (and, in all likelihood, will never release) "Game in the Sand", a 1964 short film. Not much is known about it, other than the plot concerns four children and a rooster in a cardboard box, and that there is a scene where the chicken is buried in sand up to its neck. According to Herzog, the filming "got out of hand", and he had to abandon the project. Given that his 1970 movie "Even Dwarfs Started Small" includes footage of piglets attempting to suckle on the body of their dead mother pig, chickens eating each other, and somebody being hit by a truck (all taken accidently in the course of filming), one can only imagine how bad "Game in the Sand" must get.