Whether or not Alternate History had been invented is beside the point; Richard's opponent in the battle where he died was Henry Tudor. Having Richard win instead would not be a move calculated to endear you to Henry's granddaughter, Elizabeth I, who was queen at the time the play was written.
The Simpsons did an homage/parody of Bradbury's story in "Treehouse of Horror V". The short "Time and Punishment" had Homer sent back in time to the prehistoric era, where the mere act of crushing a mosquito resulted in creating a future where Ned Flanders was an omnipotent dictator. Homer's repeated trips to the past to rectify this only make things even more bizarre. (There's one where things seem to be beyond perfect...but there's no such things as donuts. Apparently; immediately after he departs to the past, donuts start falling from the sky, and Marge remarks that it's raining again.) In the end, Homer ended up with everything normal, except that humans were now born with prehensile forked tongues.
Another version: William Tenn's 1948 short story, "Brooklyn Project". The "acting secretary to the executive assistant on public relations" describes a government time-travel experiment to a group of journalists, explaining that some scientists were foolishly concerned that a probe sent into the past might by its very presence inadvertently change the present. But this is a ridiculous notion, of course: the story ends with the journalists dissolving themselves into liquid and flowing up to examine the time travel apparatus, while the acting secretary extends his fifteen purple blobs and exclaims, "Nothing has changed!"
Another example is the eponymous novel, For Want of a Nail by Robert Sobel, in which a British victory at Saratoga leads to a very different North America. Guess where the title comes from.
The Animorphs series does this twice in the Megamorphs books. In "Elfangor's Secret', Visser Four radically alters history by changing things in the past. "Back to Before" has Crayak giving the kids a chance to not go through the construction site. Things are radically changed and they actually beat the Yeerks much faster than in the regular timeline, but at the cost of a large number of other lives in the process, (ok more lives than in the regular timeline)
What if the Skrit Na had never kidnapped Loren and Chapman? No Animorphs, no war on Earth period. What if Arbron hadn't been trapped as a Taxxon? Earth would've been successfully taken over by Yeerks.
And my personal favourite: What if a pubescent Jake had felt the need to act macho to impress his crush Cassie? Planetwide Andalite genocide and enslavement and an unstoppable Yeerk Empire.
But then, this entire trope is justified; an Ellimist did it.
SF writer Harry Turtledove is very fond of this concept. A recent short story of his featured in a mid-2007 edition of Asimov's Science Fiction magazine examined what World War II politics - up to and including the war itself - may have been like if the press had been less supportive and more suspicious, all started by a single news report basically accusing the administration of causing the bombing of Pearl Harbor through its own incompetence. However, he's most well known for a series of books featuring an entire alternate history of the United States, where the premise is that a Confederate messenger picked up a cigar he dropped. As a result, one of military history's great strokes of luck - the interception of a Robert E. Lee's complete plans for troop movements, which were wrapped around said cigar - never happened, and the whole tide of The American Civil War is turned as a result.
McClellan's most defining state in the Civil War was a massive exaggeration of the forces arrayed against him. Had he not captured the Confederate plans, which detailed the strength of the Confederate forces, he would have believed that he was massively outnumbered. (Prior to finding the orders, he thought that Lee's portion of the army held more soldiers than the entire combined forces of the CSA - in the entire war.)
This is also a running theme in his works—as the books stretch out and the timeline diverges from our own, characters will either succeed or fail at tasks by small margins, leading them to question what their lives would have been like had the event in question not happened.
In Turtledove's Atlantis series, the American Civil War is replaced with a massive slave revolt that happens partially because a slave tripped over a loose floorboard.
In The End of Eternity by Isaac Asimov, the time police exploit this professionally and with mathematical precision. The book begins with the main character changing the course of history by moving a small object onto a different shelf.
Also by Asimov (he liked this trope) is "Spell My Name with an S", where two aliens bet as to whether they could avert a nuclear war on Earth with a minor stimulus. Sure enough, getting one person to change how they spell their name works.
In the Discworld novel Jingo, Vimes' Dis-Organiser reports the events of a Alternate Universe in which Vimes decided keeping the peace in Ankh-Morpork was more important than leaving the city to chase after his suspect. The result was that the entire Watch (except Colon and Nobby) died in battle before Vetinari could complete his plan to stop the war.
Also spoofed in The Last Continent, when the wizards realize that they've been sent back in time, Ponder warns Ridcully of the potential ramifications: "The obvious thing to worry about is killing your own grandfather." To which Ridcully simply replies, "I can't see why I'd do that. I rather liked the chap."
In a different book, Rincewind remarks that killing your own grandfather is the only thing that really appeals to him in this whole time travel business.
Ridcully then goes on to point out to Ponder that stepping on insects is fine, since history-as-they-know-it either isn't affected by the deaths, or actively requires them.
This trope is played with in Night Watch- Vimes falls through a hole in time along with Carcer, a criminal; Carcer kills Vimes's mentor, Sergeant Keel, before he was able to train Vimes, but due to a few coincidences (possibly the timeline attempting to repair itself), Vimes is able to take his place as his own mentor and the leader of a rebellion. If Keel wasn't around at all, history would be very different, but since Vimes is there to take his place, causality (with a little help) manages to paper over the cracks. Also partially subverted, since Vimes actively tried to make the city better than it was, but having an Evil Counterpart on the other side, as well as Snapcase's being a bastard, kept it from going all the way.
Ridcully: I suppose we'd have settled down, had children, grandchildren, that sort of thing ... Granny: What about the fire? Ridcully: What fire? Granny: Swept through our house just after we were married. Killed us both.
The Trope Namer is referenced in Thief of Time, where there is mention of a battle which was won and the kingdom saved because Lu Tze "just happened" to be walking by the side of the road with a portable forge.
He manages a reverse of this in Small Gods by improperly cooling a key piece of a war machine. Making sure For Want of a Nail situations turn out as they should is a big part what History Monks do.
Might be a double subversion as the war was meant to happen, since that was how history of supposed to go. Lu Tze, however, decided differently...
Subverted in Mort, where the titular character spares the life of a princess who was due for assassination. Perhaps because the History Monks overlook this one, the bubble of Alternate Timeline this creates around Princess Keli (in which she's alive) gradually shrinks around her, as Destiny (in which she died on schedule) re-asserts itself. Note that having her still be alive seems to have altered the weather in her vicinity, probably as a Shout-Out to the Butterfly Effect.
In The Science of Discworld III, the wizards have to time travel around our Earth making very minor changes to prevent Darwin from being killed/never being born by the human-hating Auditors, who really want us to believe in Intelligent Design, since it eventually results in our extinction...
Hex also mentions how, in 1734, a German shoemaker named Joshua Goddelson left his house by the back door, setting in motion a chain of events that (somehow) lead to commercial fusion power in 2017.
Two Nightside novels by Simon R. Green steadily establish that the main character, John Taylor, is responsible for everything that has ever gone wrong in the Nightside, dating back to its very creation.
To Say Nothing of the Dog discusses the trope quite a bit. It has an interesting scenario involving the destruction of Coventry Cathedral. Because of cracking the Enigma Code, British intelligence officials knew in advance that it would be bombed. The novel imagines a scenario where the MacGuffin, a piece of hideous Victorian architecture, disappears during the air raid and an old busybody correctly deduces it was stolen just before the air raid by someone with prior knowledge of the raid, though she is wrong about who and why, and sends a letter about this oddity to the newspaper. When Nazi intelligence officials come across this letter, they deduce again correctly, albeit for the wrong reason that their code has been broken and adopt a new one which the Allies can't crack, and thus win World War II. The removal of the MacGuffin means that 'time' has to 'fix' things by eliminating the old busybody. The method? Send the heroes back in time to ensure she is happily married and nowhere near Coventry Cathedral.
And all of that? Is to replace yet another nail, six hundred years into the time travellers' future.
W. S. Gilbert's 1881 play Foggerty's Fairy may be an archetypal example; the protagonist makes a supernatural deal to alter his past so that he never met a certain woman. Dire consequences follow, and subsequent acts take place in alternate universes as he frantically tries to fix his past. The trope is exemplified by the words of the Fairy Rebecca:
Rebecca: And your father met your mother in this wise. Some thirty-six years ago, as he was walking down Regent Street, his attentions were directed to a sculptor's shop, in which was a remarkable monument to a Colonel Culpepper, who died of a cold caught in going into the Ganges to rescue a favourite dog which had fallen into it. An old schoolfellow passed by, and, touching your father on the shoulder, asked him to dinner. Your father went, and at the dinner met your mother, whom he eventually married. And that's how you came about. [...] If your father hadn't loitered opposite the sculptor's shop, his schoolfellow would never have met him. If Colonel Culpepper hadn't died, your father would never have stopped to look at his monument. If Colonel Culpepper's favourite dog had never tumbled into the Ganges, the Colonel would never have caught the cold that led to his death. If that favourite dog's father had never met that favourite dog's mother that favourite dog would never have been born, neither would you. And yet you're proud of your origin!
In the ingenious novel Time and Again by Jack Finney, the hero deliberately cuts himself off from the present by preventing the meeting of the inventor of time travel's parents. Why doesn't this set up a paradox? It isn't that kind of book.
The short story "Wikihistory" by Desmond Warzel has this as the reasoning behind Hitler's Time Travel Exemption Act: "no Hitler means no Third Reich, no World War II, no rocketry programs, no electronics, no computers, no time travel. Get the picture?" Hong Xiuquan, however, has no such protection.
In the short story A Little Knowledge by Elaine Cunningham in Realms of Shadow diviner cannot produce any useful prophecy because there's just too many drastic changes invoked by small causes:
Ursault the All-Seeing: Of course, if your boy Dammet remembers to tie the brindle dog when the harvest moon blooms full, the white maid will never be. A lot of trouble that will save. [...] But on the other hand, a lot of trouble that will cause. This same wolfwere maid could bring doom to the floating city. A lot of trouble that will save. On the other hand...
Cruelly subverted in the end: the villain whom Ursault allows to rob him of this burden faces an overwhelming foe omitted in Ursault's prediction, so all futures he can see are slight variations of messy overkill, obvious anyway.
Subverted in Jasper Fforde's The Eyre Affair. Thursday Next's time-traveling father asks her what happened in two important battles. In both cases the commanders were killed by an incredibly lucky shot just as the battle started. Thursday points out that this couldn't possibly be the work of French revisionists as, in both cases, the second in command took over and won the battle anyway. Her father points out that he never claimed that the revisionists were any good at it.
Only person-wide case: A brief disruption in a baby "factory" in Brave New World means that forgetting one injection on an embryo would cause him to be "the first death by trypanosomiasis for over half a century".
The premise of His Dark Materials is the Many-Worlds theory (quantum superpositions create parallel universes), and that one can travel between these worlds. Depending on when and where this split happens, this has more or less drastic effects on the world. We have: our universe; one where the Church has absolute power and souls live outside the body; one where, apparently, Britain is a Mediterranean country; one where two dust-influenced lifeforms evolved; one devoid of life; The Land of the Dead; and one where the dominant physiology is vastly different. And that's just those they visited. Good thing they never opened a portal to a universe without Earth...
The Trope Namer is referenced in the second book of Madeleine L'Engle's Time Quartet series, A Wind in the Door, when Calvin O'Keefe explains to Mr. Jenkins the reason the Ecthroi are trying to eliminate a seemingly insignificant person, Charles Wallace Murry.
All of the events of Codex Alera can be traced back to a servant girl in a rural valley wanting some flowers, by way of some coincidences and a Nice Job Breaking It, Hero moment. Otherwise, there would have been no Horde of Alien Locusts, the protagonist wouldn't have met the First Lord and gotten a scholarship to the Academy, and Lord Aquitaine's plan to become First Lord would have gone off without a hitch, ending a centuries-old dynasty but otherwise keeping the country's status quo pretty much exactly the same. Because of the flowers, though, the dynasty and rural valley survived, but almost nothing else did.
Arabian Nights tale, "What a drop of honey caused" is based off this: A hunter brings a find of honey to a merchant, but a drop falls onto the ground, which attracts insects, which attract birds, which attracts the merchant's cat, who attracts the hunter's dog who kills the cat. The merchant kicks the dog out of anger and the dog dies. The hunter kills the merchant out of anger/revenge. The merchant and hunter were from neighboring villages who fight, but the villages are either side of the border between neighboring provinces, and tit-for-tat exchanges start one of the bloodiest wars in local history, all because of a drop of honey.
In Stephen King's book Needful Things, Leland Gaunt, the proprietor of the titular shop, exchanges small treasures for ridiculously low prices if the buyer agrees to do him a small, mostly inconsequential favor. The favors inevitably snowball into large-scale disasters, culminating in the destruction of the entire town.
King also does this with ''11/22/63", where a man goes back in time to stop the Kennedy assassination and comes back to a very different 2011.
Possibly subverted in Philip Roth's book The Plot Against America, in which the Republican nomination of Charles A. Lingbergh for President in the 1940 Election keeps the US out of the war a good while longer, and massively increases antisemitism. At the end of the day, however, the Allies only win a year later than they did in real life; it's the damage to the Jewish diaspora in America, and the solidarity of the American people as a whole, that's the major outcome.
This concept is the driving force behind the events in the book A Crack in the Line. The book is about a boy whose mother is dead and who lives with his father and his mother's older sister. He accidentally finds a way to travel to an alternate timeline, where a female version of himself exists; her mother is still alive and she has no aunt. They discover that their two universes exist because of an event in the past that wasn't suppose to happen, causing the timeline to split off in two. Initially, they believe the divergence happened when their mother got in the accident which in the boy's world, killed her. However, the actual divergence happened when their grandmother, at the time unmarried to their grandfather, refused to abort the baby that would become their mother's older sister. The girl's timeline was the one created in response to this change, in which the grandmother got the abortion.
In The Never War, the third installment of The Pendragon Adventure, Bobby goes to Third Earth (Earth in the early 51st Century AD) to find out what would happen if he saved the Hindenburg. Turns out, if said Zeppelin was saved, London, DC, and New York would've been nuked by the Luftwaffe just before D Day, and things would've gone down mountain from there.
Think of what might have been. Dragon fire and savage swords in Eriador, night in Rivendell. There might be no Queen in Gondor. We might now hope to return from the victory here only to ruin and ash. But that has been averted - because I met Thorin Oakenshield one evening on the edge of spring in Bree. A chance-meeting, as we say in Middle-earth.
Alfred Bester's The Push of a Finger is built around this trope: a future-predicting machine reveals that the Universe will be destroyed in one thousand years unless the protagonists find and avert the single event that'll put everything in motion. it turns out to be a Self-Fulfilling Prophecy.
Mary Lavin's short story "The Story of the Widow's Son" is based around this, examining the different consequences of whether the titular boy did or did not accidentally run over an old hen with his bike.
In Poul Anderson's Time Patrol stories, it is carefully explained that this is not a problem, that the timeline can absorb quite a number of changes without really changing. Of course, by the same token, if someone does change it, it's hard to move back.
The novel Liverpool Fantasy has The Beatles breaking up before the release of their first single. The fallout includes, but is not limited to, England becoming a fascist state.
In the novelization of Back to the Future, Doc Brown explains it: If Marty only does so much as going to a cinema (which he knows it will close soon anyway), his 50 cents may up the income of the day/week/whatever from 999.75$ to 1000.25$, so the owner will decide not to close it, and one day it may burn down while people are in it - including a man who would have become president of the USA.
The Lord Darcy stories by Randall Garrett posit a 20th century which is somewhat behind in the physical sciences but make up for it by the practical application of magic as a scientific discipline. The turning point seems to be that Richard I survived the siege of Chaluz and produced heirs, resulting in a strong Plantagenet dynasty and a unified Anglo-French empire that has lasted to the present day. Also, somehow, magic.
The science fiction short story "What You Need" by Lewis Padgett (Henry Kuttner and C(atherine) L. Moore) features what might be called a "nail salesman." He provides, for a significant fee, rather mundane items to a restricted clientele. These items turn out to be exactly what the clients need shortly thereafter (for example, a man receives a pair of scissors, which he uses to snip his tie when it gets caught in machinery; had he not had the scissors on him at the time, he would have been killed). It was adapted into an episode of The Twilight Zone.
In the intro to A Macabre Myth of a Moth-Man, the author explains that this is how the events of the novel (including, and not limited to, several mutants and an insect-worshiping cult running around England) come about:
The year was 1944. The elements were a Polish scientist and a honeybee. In your history, the two passed without notice. One string was the divergence.
L. Neil Smith's The Probability Broach features a "North American Confederacy" which diverged from our timeline when Albert Gallatin, rather than brokering a peace to end the Pennsylvania Whiskey Rebellion leads an army against Washington and overthrows the U.S. government, creating a libertarian society. It turns out this alternate history came about because of a single word in the Declaration Of Independence, requiring the unanimous consent of the governed.
There's a chapter in What Katy Did by Susan Coolidge where Katy tries to pin the ribbon back on her bonnet, only for Aunt Izzie to insist that it must be sewn on properly. As a result, Katy and Clover are late for school and the day goes downhill from there. That evening, Katy's father recites the "For the Want of a Nail" poem to her, his point being that, if she had mended her bonnet when the ribbon first came off, she might not have had such a bad day.