Ad Astra Per Aspera has Senator Edmund G. Ross vote to acquit Andrew Johnson, leading to his impeachment in 1886. This leads to the events of three interstellar superpowers waging a galactic war in the 28th century.
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.
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.
Perhaps the most disproportionate example is the ending of Elfangor's Secret — the entire plot of the book ends up never having happened because the Animorphs were hanging out in 1969 in San Fransisco with a time machine. Not because anyone uses it, but because it ends up distracting some random hippies. One of them would have been the mother of John Berryman, Visser Four's host, but she ends up missing the chance encounter where she meets his father.
Elsewhere in the book, this trope bites Visser Four in the ass. His plan involves interfering with human history to affect the outcome of crucial battles, including the Invasion of Normandy, the Battle of Agincourt, and assassinating Albert Einstein. However, as more events are altered, the timeline becomes vastly different and unrecognizable, eventually culminating in the Visser demanding access to Einstein's chambers at Princeton University, now no longer in the United States, while the physicist is in Germany doing nothing in particular.
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 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.
There is a Dr. Seuss book called Because A Little Bug Went "Ka-choo!"wherein a bug sneezes, causing a seed to fly off a plant, conking a turtle on the head, causing said turtle to fall into a pond, causing a chicken to get wet...well, to put a long story short, it leads up to a farmer getting a bucket stuck on his head, a boat sinking, all the aforementioned characters and items, along with the police and a fire engine, colliding with an incoming circus. They all go hurtling into the city, and the whole city is thrown into utter chaos...all because the little bug went "ka-choo"!
Only person-wide case: A brief disruption in a baby "factory" in Brave New World means that forgetting one injection in one embryo would cause him to be "the first death by trypanosomiasis for over half a century."
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!"
In A Brother's Price Corelle's crush on the neighbour's boy kicks of a chain of events that eventually leads to Jerin marrying the princesses of the realm. If she hadn't had a crush on Balin Brindle, she would have been the one to save princess Odelia, none of the princesses would have ever seen Jerin, and everything would have happened differently. Also, in the backstory, princess Ren survives an explosion because she cries at a sad scene in a play, and is sent outside by her abusive husband, Keifer. And of course, everything would have been different if Prince Alannon had not worn a specific piece of jewelry when he was kidnapped. And the war in which the kidnapping happened would never have been fought if one man hadn't been infertile.
In the Chaos Timeline, Genghis Khan dying from a minor accident in 1200 prevents the unification of the Mongol tribes and their subsequent global conquests. The world becomes very different...
In one Children of the Lamp book, a police officer saving Philippa from being hit by a bus set off a long chain of events that resulted in a volcano erupting and incinerating her mother's body.
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.
The humans of Amusehorn in Cooking With Wild Game have evolved similarly to their cousins on Earth although they never domesticated dogs (and, in fact, consider them fictional). Horses' nonexistence doesn't change things either, although that's more explicable because the Totos species is used for long-distance transportation instead.
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 supposed 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.
Decades of Darkness has President Thomas Jefferson dying of a heart attack. His bumbling successor James Madison manages to anger the New England states enough so they leave the Union and defend themselves successfully in a war, splitting the USA forever. The slave states get the majority and transform the rest into an expansionist slave-holding empire.
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, Nobby, and Angua) 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 Discworld- Vimes falls through a hole in time along with Carcer, a criminal. Carcer kills Vimes's mentor, Sergeant Keel, before he is 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 was 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.
The Divine Comedy: Paradiso breaks the fourth wall at one point to remind the reader that if the sun or the planets or even the stars were aligned slightly differently, every living being on Earth could be dead.
"Behold how from that point goes branching off / The oblique circle, which conveys the planets, / To satisfy the world that calls upon them / And if their pathway were not thus inflected, / Much virtue in the heavens would be in vain, / And almost every power below here dead."
In Dragon Bones, there are several. For example, the king's bastard brother, Alizon, takes a sip of water to get rid of the bad taste that talking about the king leaves in his mouth ...which makes him be just a tad bit late to avoid the murder of a nobleman at the hands of the king. Said event significantly contributes to the revolution that is in the making.
Most of the problems in The Dresden Files can be traced back to the moment where Harry Dresden interviewed the Red Court vampire Bianca. He started bleeding, causing her to lose control and attack him. He defends himself, and later she's emotionally out-of-control enough that she accidentally kills one of her thralls. Since the Red Court runs on Evil Is Petty and Never My Fault, she decides that it was Dresden's fault the girl died and becomes a Red Court noble as part of her plan to get revenge on him. At the party for her induction into nobility, she gives multiple people gifts and springs a trap designed to force Harry into either letting her get away scot-free or starting a war between wizards and vampires. He chooses Door 2, and the Vampire War ends up having huge repercussions throughout the rest of the books, and only ends when Harry kills every single Red Court Vampire. Her gifts are also important. The gift she gives to Lea ends up infecting her and later Maeve with Nemesis, leading to the plot of Cold Days, and the gravestone she gives to Harry provides him a sanctuary so he could survive while he was a ghost.
The End of Eternity: 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.
"What If (1952)": When Mr. What If shows Norman and Liwy what life would've been like if they hadn't met on a streetcar, they find that they got engaged to completely different people. Norman had even married Georgette, while Liwy was dating another of their friends.
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 have been 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.
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!
For All Time: Barely two weeks after Pearl Harbor, FDR suffers a fatal stroke. His far less competent successor, Henry Wallace, manages to screw things up both domestically and internationally. This sets the stage for the emergence of a truly insane Crapsack World.
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 Girls is a Roman à Clef about the Manson Family and the Sharon Tate murders. In the book, Evie joins the others on the ride to what will soon be the Edgewater Road murders. Evie touches her girlfriend Suzanne's hand, Suzanne is snapped out of a reverie, and Suzanne immediately dumps Evie on the side of the road, a half-hour before they arrive at the murder scene. Evie's left wondering for the rest of her life why Suzanne ditched her by the side of the road—whether it was because she realized Evie couldn't kill, or if it was because she realized Evie could kill, and so she dumped Evie so Evie would have the life Suzanne wouldn't.
Gravity Falls: Journal 3: One of the dimensions Ford passed through was a parallel timeline where Stan didn't knock Ford into the portal. Its version of Ford reunited with McGucket, got the portal to work without any risk of allowing entry from the Nightmare Realm, and became well-regarded for his work in the scientific community. This was where he got that BFG he tried to use in "Weirdmageddon Part 1", from Parallel!McGucket.
We learn in Harry Potter and the Goblet of Fire that the Marauder's Map is unable to distinguish between two people who have the same name. If the Marauders had thought of that, Harry would have seen that Barty Crouch Jr. was the one sniffing around Snape's office. If he had, he would have learned that Barty Crouch Jr. had been a Death Eater, and then possibly Voldemort would never have been resurrected and a whole lot of misery would've been avoided.
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...
Lampshaded at the chance meeting between Madam Thenardier and Fantine. "If the madam had been standing, events would not have played out as they did..." Victor Hugo underlines the fact that Madam Thenardier was quite big and scary standing up. Because she was sitting, Fantine found her more affable, and left Cosette with her.
More than once during the battle of Waterloo sequence: A rainy cloud on the morning of June 18 changed the world (postponing the battle for two hours, giving Blücher the opportunity to arrive in time). Later on, a farmer acting as Napoleon's guide, shook his head, making Napoleon order an entire cavalry unit riding straight into a causeway. "If this farmer had not done this..."
In the short story A Little Knowledge by Elaine Cunningham in Realms of Shadow, a diviner cannot produce any useful prophecy because there's just too many drastic changes invoked by small causes. 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.
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...
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.
Look to the West's very different world (Steampunk revolutionary France, a divided India, French Australia, loyalist America) all stems from George II tripping on the carpet at his coronation in 1727.
In the intro to A Macabre Myth of a Moth-Man, the author explains that this is how the events of the novel (including, but 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.
The Lord Darcy stories by Randall Garrett posit a 20th century which is somewhat behind in the physical sciences but makes 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.
In the appendices of The Lord of the Rings, Gandalf theorizes how the story might have been completely different, if Smaug the dragon had not been killed in The Hobbit.
"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."
In Lunatics, the entire plot could have been avoided if Horkman had not called Peckerman's daughter offsides in a peewee soccer game. As a result, Peckerman goes over to Horkman's house later, which results in a high-speed car chase, expeditions overseas, and even a stint onstage at the Republican National Convention for the both of them after things keep getting progressively more out of control.
The Martian features these kind of scenarios regularly, in order to underscore the need for utter perfectionism in space travel and how catastrophically things can go wrong from even the most minor defects. Of particular note is the loss of the Iris probe, which fails when, in order:
1) A minor fuel imbalance in the rocket causes an unplanned vibration in the payload during launch. 2) A load of protein bars undergo liquefaction of their vegetable oil due to the added stress of the vibration on top of the G-force from the launch itself. 3) The second stage engine ignites one second too soon, not giving the protein bars time to re-solidify. 4) The probe's center of mass winds up slammed to an unexpected location from the craft's acceleration, placing tremendous stress on a single bolt, which shears from the load. 5) Due to an almost invisible minor defect in another of the six bolts, it shears as well from now having to handle the load of the destroyed first bolt in addition to its own. 6) The remaining four bolts simply aren't enough to distribute the weight and break as well. 7) Iris rips itself apart from the inside out, utterly destroying the probe.
A More Personal Union begins when a young man recovers from a mid-autumn cold. The young man is the king of France, and the cold would have killed him. Instead, he lives for another seven years, and his continued reign brings very big changes to France.
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.
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.
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.
No Spanish Civil War in 1936 sees a (non-Stalinist) leftist Republican Spain not only survive the attempted coup in 1936 (with Francisco Franco critical to the thwarting of that plot), but become a junior partner of the Allies when World War II rolls along, having an anarchist (Buenaventura Durruti) for a president, and great advances in Spanish influence in the arts of the mid-20th Century, all because Casares answered a letter from Franco that didn't go answered in real life.
"The Pierce-Arrow Stalled, and..." by Kim Newman imagines a world where the stalling of the eponymous car means that Fatty Arbuckle never makes it to that party, which in turn means that Will Hays doesn't think Hollywood is entirely a sink of depravity that needs a code. Events branching out from this include Joseph Kennedy becoming President (because Hays stood for the Republicans and lost) and John Dillinger evading the law (because his girlfriend was so disgusted by the movie the police intended to catch him at that they left early).
In the novel The Post Birthday World, Shriver explores this trope when her protagonist has a birthday celebration with Ramsey, a friend of Lawrence, her partner. In one storyline, they kiss and she ends up leaving Lawrence for Ramsey. In the other, she avoids it and stays married to Lawrence. The novel explores what happens with each man.
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.
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.
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.
In Sky Jumpers, Hope loses her "perfect potato" for her invention, a hand crank-operated potato peeler, on her tram ride to school. In desperation, she goes to the lunchlady, who can only offer some less-than-stellar ones. Hope ultimately settles for one of them, but when demonstrating her invention to her class, it comes apart, leaving her with a jagged piece of wood in her hand.
When Heather and Veronica get zapped into the novel The Queen of Twilight in The Wizard, the Witch, and Two Girls from Jersey, the original protagonist of The Queen of Twilight gets killed and Heather is mistaken for said protagonist. Veronica hopes they can just reenact the original plot in order to survive and get home, but between 1) Heather being very different personality-wise from the original protagonist, and 2) the "princess" now having an outspoken "handmaiden" (Veronica), they end up taking a different route on their quest, with a different elf accompanying them, with the titular wizard dead...
In  this trope is weaponised: DODO operatives go back in time to make subtle alterations to history so that events centuries later are to the advantage of the USA.
The entire plot of Son essentially happens because Claire's handlers forgot to get her back on the pills distributed in the Community after her reassignment to the Fish Hatchery. The pills are meant to quash strong feelings, and, without them, she starts developing an attachment to the son she was forced to produce as a Birthmother. Because of her feelings for Gabriel, Claire runs away from the Community and eventually makes a deal with the Trademaster to find him again. In turn, this leads to Gabriel defeating the Trademaster for real (compared to his simple banishment after the previous book's ending). If someone had just remembered to give Claire a new bottle of pills, none of that would have happened. Claire hypothesizes that everyone simply assumed that someone else told her to do it.
A Sound of Thunder, by Ray Bradbury, in which stepping on an actual prehistoric butterfly changes modern politics for the worse (see In Spite of a Nail, though). The story does suggest that time-travel in this future period is very expensive with stiff fines for ignoring the plainly-stated safety rules, which the protagonist foolishly ignores, causing the accident. Presumably, the expense is supposed to ensure only competent citizens use it.
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 thing 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.
Leo Tolstoy's short story "A Spark Neglected Burns the House." A hen flew from one neighbor's yard to another and laid a few eggs. The owners of the yard went out to collect said eggs, but the first family accuses them of stealing. An argument ensues that results in both families bringing up every nitpick between them for generations back. The feud eventually escalates, and before you know it, one family has set the other's house on fire. The fire spreads back to the other family's house. The feud had gone on for so many years and had become so public that no one in the village helps out, and both families lose everything in the fire. Eventually, both families reconcile and rebuild their homes. The moral of the story was to "quench a spark before it becomes a fire".
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 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.
Time and Chance, a novel about a man whose name is Richard Cochrane and who made the choice to leave his small country in order to become a famous artist. Elsewhere, Rick Cochrane decided instead to stay in his hometown and have a family. The two characters are the same man but with differents choices exchanged their places.
Subverted in the Choose Your Own Adventure spinoff novel Time Machine: Search for Dinosaurs. Your character travels back to the Mesozoic Period and encounters a troublesome rodent in their tent. At first he/she decides to kill it but then decides against it, reasoning that this small action could have disastrous consequences on future species.
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 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.
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.
SF writer Harry Turtledove is very fond of this concept. A 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 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.
The Union and Liberty timeline begins with a small change in Andrew Jackson's 1828 campaign platform and changing a few words in a John Calhoun speech.
The Warcraft Expanded Universe novel Thrall: Twilight of the Aspects shows an alternate history in which Thrall had been killed along with his parents when he was a baby. In this timeline, Aedelas Blackmoore, without his "build army of orc slaves" plan, was forced to sober up, and became an even more dangerous individual. He killed Orgrim Doomhammer, Taretha Foxton is still alive, but is abused by Blackmoore. Krasus/Korialstrasz is also still alive in this timeline, having sacrificed himself at the beginning of the novel. Oh, and Kel'Thuzad is Blackmoore's advisor now, instead of a Lich. The Scourge never invaded, which means Arthas never had his HeelFace Turn into Death Knight, the worgen were never unleashed to combat them, Lordaeron is still intact, the Sunwell was never destroyed, which in turn means blood elves don't exist. The list goes on, find the For Want of a Nail entry on the main page for more. All because Thrall was never found by humans.
In The Watchmaker Of Filigree Street, the title character has a form of precognition that includes being able to see these moments, and his memory alters itself depending on how they turn out. For instance, he "remembers" a piece of music, but forgets it when Thaniel doesn't acquire the sheet music for it.
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.
The science fiction short story "What You Need" by Lewis Padgett (Henry Kuttner and C. 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.
The children's story Why Mosquitoes Buzz in People's Ears: A West African Tale a mosquito lying leads to a chain of events where the sun does not rise.
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.
The Wild Cards universe is partially built around this idea. In 1946, a pulp-style villain named Dr. Tod releases a genetic virus over New York, which leads to a world where about 9% of the victims have superpowers or other such mutations. As a result, the 1980s global political landscape and social issues are changed radically: the Arab-Israeli Wars were averted thanks to an Ace who was able to make a peace agreement happen, Mahatma Gandhi was saved from assassination in 1948 only to see his efforts to unite India fail because there is no common reaction to his death, Joseph McCarthy went after superpowered people as well as Communists, Fidel Castro remained a baseball player, Guevara's attempted revolution in Cuba was quashed and left Batista in power into the 1980s, Buddy Holly lived to become a has-been and then a shaman ace, Marilyn Monroe lived past the early 1960s, Elizabeth Taylor died instead of James Dean in their car crash, and the Civil Rights Movement involved superpowered people alongside other minorities.
In The Curse of Chalion, after Cazaril realizes the extent of the gods' manipulations, he wonders how many men they sent on the road to help Teidez as he was sent to help Iselle, and who never made it. In Paladin of Souls, the Bastard confirms to Ista that the Son of Autumn sent many, but all failed.
In Paladin of Souls, a prayer to the Bastard calls this trope explicitly, with indication that it's divinely inspired at the time:
"And the Bastard grant us...in our direst need, the smallest gifts: the nail of the horseshoe, the pin of the axle, the feather at the pivot point, the pebble at the mountain's peak, the kiss in despair, the one right word. In darkness, understanding."
The Yiddish Policemans Union takes place in an alternate universe where one Congressman is hit by a car in 1940. As a result, the state of Israel is destroyed soon after its birth and the world's last Jewish redoubt is in the Alaskan panhandle.