I am thinking of the suggested use of ze as an alternative for he or she. I cannot think of an example where such a thing has actually been adopted and put to general use.
New words, or neologisms, are almost always intentionally introduced and adopted into the English language. Here are many that have recently been added to OxfordDictionaries.com, including selfie stick, cryptocurrency, and binge-watch. These words were not accidentally introduced to the English language, but rather done so for a purpose — namely, to allow us to speak of things as yet unnamed.
While ze has not yet been accepted by the mainstream, words like cisgender are in the process of becoming accepted and words like bikini have been accepted. Every word, at one point in time, did not exist and was therefore created to fulfill a particular purpose; however, not every word created has gained widespread use.
If you are truly curious, I suggest looking up any word's etymology.
As a side note, this reminds me of the children's book Frindle, which is about what would happen if a child decided he was going to start calling pens frindles. That won't give you any answers, but it might be nice to read.
Ms. is probably the most obvious example.
(plural Mses.), 1949, considered a blend of Miss and Mrs. - Etymonline
Prior to the feminist movement of the mid-1900s, women were either Miss (unmarried) or Mrs. (married, widowed, or divorced). In contrast, men of adult age were always Mr., regardless of marital status. It was felt that it was insulting to women to be so defined and characterized by marital status when men were not. Ms. (pronounced "miz") was a manufactured alternative introduced. At one time, its usage was considered a somewhat controversial feminist statement. But by now it has largely replaced Miss and a significant number of married women use it, too.
Yes, there are. Gay comes to mind (from etymonline.com):
The "Dictionary of American Slang" reports that gay (adj.) was used by homosexuals, among themselves, in this sense since at least 1920. Rawson ["Wicked Words"] notes a male prostitute using gay in reference to male homosexuals (but also to female prostitutes) in London's notorious Cleveland Street Scandal of 1889. Ayto ["20th Century Words"] calls attention to the ambiguous use of the word in the 1868 song "The Gay Young Clerk in the Dry Goods Store," by U.S. female impersonator Will S. Hays, but the word evidently was not popularly felt in this sense by wider society until the 1950s at the earliest.
My understanding is that the gay community had had enough of having only derogatory or clinical terms to describe their sexual preference and chose to use a word that simply meant happy. The usage later percolated to the rest of society.
In technical writing, this phenomenon is very common. An author will publish a paper describing a novel process/moiety/species or whatever, and their chosen name for it is usually accepted by the rest of the scientific community. Off the top of my head, I can think of wobble position coined by Francis Crick. There are easily dozens of similar examples in science.
Robert Hendrickson, The Facts on File Encyclopedia of Word and Phrase Origins (1997) has this entry for the word quiz:
quiz. A short test. The tale may be apocryphal, but it's said that in the late 18th century Dublin theater manager James Daley bet that he could invent and introduce a new meaningless word into the language almost overnight. He proceeded to pay Dublin urchins to chalk the word quiz on every wall in town. By morning almost all Dubliners had seen the word, and because no one new what it meant, the meaningless quiz became the word for a "test of knowledge."
It's an amusing story, but it has a chronological problem: according to Merriam-Webster's Eleventh Collegiate Dictionary (2003) quiz first appeared in English in 1749—which is a bit early for a "late 18th century" theater manager to have dreamed it up. On the other hand, the earliest two definitions that the Eleventh Collegiate gives are "1 : an eccentric person" and "2 : PRACTICAL JOKE," both of which seem fairly relevant to the story that Hendrickson repeats. The Eleventh Collegiate contents itself with reporting quiz's etymology as "origin unknown."
Of the Dublin story, Glynnis Chantrell, The Oxford Dictionary of Word Histories (2002) rather sourly writes, "There is no evidence to support this theory." There is, however, a rather striking parallel mystery surrounding the word quoz. From Charles Mackay, Memoirs of Extraordinary Popular Delusions and the Madness of Crowds, volume 2 (1841):
Many years ago the favourite phrase [in London] (for, though but a monosyllable, it was a phrase in itself) was Quoz. This odd word took the fancy of the multitude in an extraordinary degree, and very soon acquired an almost boundless meaning. When vulgar wit wished to mark its incredulity, and raise a laugh at the same time, there was no resource so sure as this popular piece of slang. When a man was asked a favour which he did not choose to grant, he marked his sense of the suitor's unparalleled presumption by exclaiming Quoz! When a mischievous urchin wished to annoy a passenger, and create mirth for his comrades, he looked him in the face, and cried out Quoz! ... Every alehouse resounded with Quoz ; every street-corner was noisy with it, and every wall foe miles around was chalked with it.
But like all other earthly things, Quoz had it season, and passed away as suddenly as it arose, never again to be the pet and the idol of the populace.
So neither quiz nor quoz is a perfect example of a word devised and propagated for the amusement of its originator, and yet both have enough hints of such an origin to (if nothing else) support quite old popular stories to that effect.
On a more recent (and less fanciful) level it seems highly probable that laser as an acronym for "light amplification by stimulated emission of radiation" was coined (in 1957) with the fully formed idea that it would serve as a new and handily simplified name for the technology.