Before Thomas Bowdler got a reputation one would have refered to this trope as the castration of stories. This means that the term "bowdlerization" is itself a bowdlerization.
Bowdler's reasons for editing Shakespeare bear examination. It was once common for well-bred women and girls not to be allowed to read Shakespeare (or any secular author, for that matter), as it was thought that exposure to robust prose would render a lady "coarse" and "unfeminine". Bowdler's edited versions were the first serious non-religious fiction many young women were allowed to read. Although Bowdler hoped that his target market would eventually be permitted to read Shakespeare unfettered, it was not until the 1930s that daughters of noble families were generally allowed full access to the Bard's works.
Note that Lewis Carroll (in the preface to "Sylvie and Bruno") thought that far more should be cut out of Shakespeare than Bowdler had cut ("I am filled with a deep sense of wonder, considering what he has left in, that he should have cut anything out!"); again, he was talking about a version of Shakespeare suitable for girls aged 10 to 17.
When Vice Admiral Horatio Nelson was dying at the Battle of Trafalgar, he said "Kiss me, Hardy", Hardy being the captain of the ship he was on board, and the de facto fleet commander with Nelson in his condition. Apparently this was far too homoerotic for school children, so certain sources relate his words as "Kismet, Hardy". Which completely ignores the fact that Hardy did kiss Nelson (on the cheek).
Important officials have often had quotes bowdlerized by those reporting on them (for face-saving purposes, most of the time).
John Nance Garner IV, a Vice President of the United States under Franklin Roosevelt, once described the office (as reported) as "not worth a bucket of warm spit." The word he really used was "piss", and (according to TOW) he "once described a writer who quoted it this way as a 'pantywaist'."
Ronald Reagan, after finally pushing legislation through Congress permitting the sale of AWACS to Saudi Arabia (the Congress and the pro-Israeli lobby were strongly against it), said, "Thank God!" according to his Deputy Chief of Staff. What he actually said, according to someone in the room, seems more in line with his personality: "I feel like I've just crapped a pineapple."
While it's a general rule that race horse names can't be changed once a horse has started, exceptions have been made when the name was found to be unsuitable after the fact. Heesaputz raced for several years before the Jockey Club discovered that "putz" means "penis" in Yiddish, so they asked the owner to change the name. Heesaputz became Samuel Alan. Similarly, Heart On became Heart One due to a double entendre, and Columbine Is Sad became Dake after the Columbine shootings. The funniest example was Liquor In Excess. That name was vetoed by the Jockey Club due to a double entendre, so it was changed to Censored.
The Pirates of the Caribbean ride at Disney Theme Parks suffered this over the years. The Pirate that originally was looking for a young girl whose underthings he snatched was commenting how spry she was — with her head poking out from the barrel behind him. His lines were toned down, underwear taken away. Then it got changed to the pirate looking for Jack Sparrow.
The portly woman chasing after hot pirate tail was changed to her chasing with a rolling pin after pirates who stole her pies.
The whole scene was changed — all the pirates are being chased by women for stealing their food (the rooster chasing the hen appears to be fine).
However, the scene where pirates are selling women, with a banner proclaiming "take a wench for a bride" remains.
Another Disney Theme Park example: the face character version of Kida is actually shown there in a long flowing dress instead of in a bikini and a sarong like in her movie (in the actual film, that dress only appeared in the ending).
In 2007, Goldman Sachs were selling selling securities they knew were bad and, more or less, betted against those securities. An email from Goldman senior executive, Tom Montag, was brought up at a Senate hearing. In his email, Montag remarked of the Timberwolf I security, "[B]oy, that timeberwof [sic] was one shitty deal." Senators Carl Levin and Susan Collins proceeded to refer to these securities as "shitty deals." Every newscast covering the story except one bleeped the word "shitty." In order to prevent this from ever happening again, Goldman Sachs put up a email filter that blocks swear words.
General of the Armiesnote Note the plural; this is technically the American Army's highest rank, held only by Gen. Pershing. The only higher rank, General of the Armies of the United States, note the added words, was invented specifically so they could posthumously promote George Washington so he'd hold a higher rank than any active-duty general. John "Black Jack" Pershing, whose original nickname now requires N-Word Privileges.
When Japan was originally opened to the West, there came a serious interest among Western intelligentsia for Japanese literature and mythology. What they got didn't always sit well with them—in particular, the "Kojiki", perhaps the most important collection of Shinto stories. The way in which Izanagi and Izanami created the gods and islands of Japan — sex — was far too vulgar for the Victorian audience, and was excised from the first English-language translations.
That picture of the David statue with the boxer shorts on the main page? It was clearly done in jest, but something like that actually happened. A plaster cast of the statue was made as a gift to Queen Victoria, and since this was one of the more prudish times in history, they felt that male nudity might offend someone, so a plaster fig leaf was made to use during the Queen's visits.
A similar example: a cardinal once had plaster leaves placed over the genitals of a collection of naked Roman statues in a musesum. In order to make them fit, he actually had to go through the museum and chisel off parts of their penises.
The discontinuation of lingerie for Barbie dolls in the late 2000s.
The word "hexadecimal" is a bastardisation of Latin and Greek roots, and exists only because the more etymologically-correct "sexadecimal" was raising titters among computing pioneers.
After The Second Google Incident, commands from the advertising that keeps the site afloat mandates that This Very Wiki either eliminate trope pages for more sexually explicit works or find new (much less family friendly) sources of funding. A number of works the sexual explicitness of which is debatable (most prominently Lolita, which has since been restored, and It, which does feature underage copulation in one scene but otherwise contains little explicit sexual content) have been caught in the mass deletions.
An unacknowledged, but widespread, term used off-the-record by biologists to describe otherwise-monogamous birds which engage in covert extra-pair copulation, or male animals (salmon, cuttlefish, etc) that use deceptive coloration and behavior to approach females without the dominant male noticing them, is "sneaky fuckers". Not something you'd ever see in a Nature article, but notations of "SF" turn up in a lot of field notes.
Way back in 1971, Dodge introduced a car called the Dart Demon, complete with a cartoony pitchfork-wielding devil as its mascot. Some Christian groups complained and two years later the devil mascot was abolished and the name was changed to Dart Sport.
Actor Benedict Cumberbatch invoked this on the fanbase, the Cumberbitches. After Benedict expressed some discomfort at that name, his fans, out of respect (and since some of them didn't like calling themselves "bitches" in the first place,) started using the more benign "Cumberbabes" more and more.
The subtitles on Netflix seem to censor some of the swearing. For instance "fucking" was changed to "kissing" on an episode of United States Of Tara
The most common name for the Common Moorhen (Gallinula chloropus) in Spanish is "polla de agua" ([female] water chicken). As "polla" has become increasingly more used as a slang for male genitalia, many Spanish bird guides have switched to "gallineta" (small hen).
Movie fans living in Barbados in the 1980s were treated to newspaper advertisements for Doctor Detroit with the tagline "He's got five personalities. And they've all got a one-track mind" crudely changed to "He's got five lovely women. And they've all got a one-track mind." The (literal) scissors came out even further for The Best Little Whorehouse in Texas, with one part of the title - no prizes for guessing which - being cut out and replaced with "Fun."