Dammit! I knew I shouldn't have left that tap running back in 1932.
The first rule of time travel is that any and all modifications made to the timeline result in Hitler winning World War II. Run over a hippy in 1968? Hitler wins.
— colonel_green, ScansDaily
As the amount of time-traveling you do increases, the probability of Hitler winning World War II approaches one.
You return home from your jolly time travel adventure in ancient Greece, having saved the world and being careful not to upset history and.. hold on a moment? Are those swastikas?! Hanging from the White House?! Looks like you've been hit by Godwin's Law of Time Travel.
Talked to the wrong person? Nazi victory! Left technology back before the dinosaurs were wiped out? Nazi victory! Stepped on a bug? Nazi victory! Left a tap running? Nazi victory! Prevented a Nazi victory? Nazi victory!
About the only time travel that doesn't result in a Nazi Victory is traveling to times after WWII (including the future)... unless a Neo Nazi steals your timetravel pod from you to help out Hitler.
The strangest thing about Time Travel is probably that a) the Nazis winning WWII is the most common accidental timeline shift and b) that will usually be the only change in the new timeline. It almost seems like Germany was supposed to win, and that history is trying to snap back to its original form. Perhaps Germany actually won, and a neo-ally traveled back in time to make sure the Allies won by making Hitler depressed or convincing him to declare war on the one (overwhelmingly isolationist) nation whose industrial potential outstripped all the other first world countries combined.
Interestingly, in reality, a Nazi victory (though depending on how one actually defines "victory") seems to have been quite improbable. The Allies were in reality much more powerful in many ways— including both population and industrial capacity— than the Axis. There was no single, easily changeable factor contributing to the Allied success, and it is likely that many changes to history would be needed for Germany to have a decent chance of winning. Even if they won, if you are Continentalist-historian then you'll argue that Hitler never plotted to Take Over the World and just wanted a German superstate dominating Europe, so the United States and many other countries probably wouldn't have been flying the Swastika (and not even taking into account that the history of American wars on its home continent contains enough guerrilla warfare to rival the methodologies of the Viet Cong).
Godwin's Law of Time Travel can also be used in telling similar stories about other past war-losers and faded empires. The Confederacy, the Soviets, the Romans, the Greeks, the Egyptians, the Aztecs, and the colonial-era British are all possibilities. The Nazis are by far the most dominant in this field, however. Other than in steampunk, that is (but steampunk universe usually happens without time-travel).
When the time traveler deliberately tries to avoid Nazi victory and inevitably fails, it's Hitler's Time Travel Exemption Act.
After 52, Earth-X is reborn as Earth-10. The Superman of Earth-10 is named Overman (literally, ‹bermensch) and is rather upset that he came into his powers after the Nazis won; there's nothing for it but to turn the Nazi Empire into as much of a Utopia as he can make it.
Marvel Universe: Hauptmann Englande was a version of Captain Britain from an alternate universe where the Nazis won WWII.
There is also the novel trilogy The Chaos Engine where the Red Skull uses a Cosmic Cube to create this reality...or so he thinks. In reality, the Cube is faulty and works by searching alternate realities and merging elements of them together, or entire alternate universes depending on the scale of the wish. Thanks to the wish, the Nazi's not only won World War II and conquered the planet, they rule an expanionsist, tyrannical and genocidal intergalactic empire under the Skull's leadership.
In About Time Tim's dad explains that since it's Mental Time Travel, Tim can't change events from before he was born, and names killing Hitler as an example.
Subverted in Animorphs. In one book the villain goes to several points in time to make humanity easier to conquer in the present. While the Animorphs are following him the villain makes a stop at D-Day to make sure Nazis win. But thanks to previous changes there are NO Nazis at All. What everyone finds is an English force invading a France-Germany alliance, no one can figure out which side has the good guys, and Hitler is just a driver of a jeep.
While it may be true that the actual Nazis didn't win, we still start off in an alternate-timeline-present that has America (including the Animorphs) in a very nazi-like state, where everyone's racist and whatnot.
Ray Bradbury's A Sound of Thunder has a time traveler stepping on a butterfly in the Mesozoic era cause a fascist dictator type to win an election. Not actual Nazis but the dictator's name is Deutscher, which seems close enough to A Nazi by Any Other Name, particularly for a story written in 1952.
In Dean Koontz's Lightning, the Nazis themselves attempt this. They built a time machine and traveled into the 1980s to learn how they will lose the war, as well as arm themselves with some modern weapons.
The book Making History features the protagonist sending a pill to cause male sterility back to the water supply of the village where Hitler would be born, erasing him from existence. Naturally, his absence during an incident in the trenches of the First World War results in the survival of a German soldier who would normally die, and he goes on to become a fascist, anti-Semitic dictator anyway—except he's smarter than Hitler, so he wins World War Two. The protagonist wakes up the next day and finds that he's in New Jersey rather than England, his grandparents having fled England in the face of a Nazi invasion. Major changes this has on the United States are that the anti-Communist paranoia during the Cold War is shifted against the Nazis, and that homosexuality is outlawed. This world also has much more advanced computing and electronics, for unknown reasons. There are a variety of other small differences mentioned.
Horrible dramatic irony pops up because the poisoned water supply is later used to sterilize Jews and other undesirables.
Played with in "Missives from Possible Futures # 1: Alternate History Search Results" by John Scalzi. None of the alternate histories described result in Germany winning World War II (in most of them World War II never happens at all) — but a quarter of them result in Germany winning World War I.
Subverted in Roger Zelazny's Roadmarks. A highway runs from one end of time to the other with offshoots that lead to alternative time lines and poor Hitler still can not find the place "where he won."
In the setting of Connie Willis's time travel stories, the danger of Nazis winning World War II is catastrophic, because in the backstory, the inventor of time travel was a descendant of Holocaust survivors, which would mean time travel would never exist in the first place. In Blackout/All Clear, the protagonists spend a lot of time worrying that whatever little thing they do will make the Nazis win.
Warlords of Utopia by Lance Parkin, a novel in the Faction Paradox universe, has all the Alternate Universes where Hitler won declared war on all the Alternate Universes where ancient Rome never fell.
Inverted in Michael Chabon's The Yiddish Policemens Union, which takes place in an alternate timeline where Hitler got his ass kicked even harder than he did in our world. Among other changes, Germany was nuked at the end of the war, and the Holocaust killed only a third as many Jews as it did in Real Life. The book explores how these events (coupled with the subsequent collapse of Israel in 1946) make life more difficult for surviving Jews.
Live Action TV
Spike.TV produced a tv special called Alternate History, talking about Nazi America in a realistic light and how it could have happened. It shows that Hitler could have made certain decisions or invented certain technologies [like nuclear weapons] that would have defeated the USA. The USA, now Nazi America, is similar to USA of today except under totaltarian rule and all non-white Americans are slaves or racially targeted to the point that many Americans ironically want to move to Mexico [instead of today where its vise versa]. The lack of liberty and large non-white populations of America causes a civil war where [ironically] the American people become terrorists against the government.
In the 1980 series Darkroom, a man finds that he can send morse-code messages to a ship during WWII. He tries to give the United States an edge by telling them information from history-books— and the next day he opens the door to see a Nazi-parade, since Hitler had won and the Nazis now ruled the world.
One skit features George Foreman accidentally traveling back in time, where he's challenged to a boxing match by Hitler. Foreman of course wins, becomes the new Furher, and then conquers the United States.
Another skit shows an infomercial for the "Timecrowave," a device that sends TV dinners back in time simply to heat them up. When (Alec Baldwin) accidentally puts in a chicken dinner despite getting a roast beef dinner a minute before, several visual gags show history having been altered. One of those gags has Nazi banners hanging on the houses seen through a window.
Averted on various alternative Earths. In all their travels, they never went to a world where the Nazis won and conquered the world. The closest ones were the world in the episode "California Reich" (where the United States is run by white supremacists and non-Aryan people are turned into slave labor cyborgs), and the Cold War World in the pilot episode (where the USSR rules the world).
Of course, there were several worlds where the Kromaggs were in power, and they were indisputably A Nazi by Any Other Name.
This happened in the first episode of Time Cop the TV series, complete with the hero going back in time to prevent the Nazi Future by stopping the Nazis from getting the atomic bomb.
Parodied by The Whitest Kids U Know. Apparently, just resetting your internet history is enough for Nazi zeppelins and Nazi dinosaurs with laser eyes to appear.
In the Big Finish Doctor Who audio "Colditz", a minor character reveals that she's from Britian in the 1960s — controlled by the Nazis due to the Doctor's appearance in Colditz Castle. The line of causality ends up being quite confusing.
The Doctor: "The German Reich!? Hahaha, I should have known. The oldest paradox in the book!"
Part of the premise of the play Copenhagen, although it's less a case of time travel and more a case of historical figures looking back from the afterlife and speculating about what might have happened if they'd done things slightly differently. The main focus of their speculation is a meeting that took place in the early part of WWII between the two main characters, good friends Bohr (who wound up working for the Allies) and Heisenberg (who was working for the Nazis), when both were hovering right on the verge of making a breakthrough that would lead to the development of atomic weapons, but neither had quiiiiiiiiiite hit the necessary Eureka moment yet.
In Command & Conquer: Red Alert, Einstein creates a time machine so he can kill Hitler, but returns to find that World War II still happened, except this time it was the USSR that invaded Europe. It is referred to as the Great World War II in the manual and is said to have been many times more destructive than our World War II.
Red Alert 3 takes this even further: just as the USSR is about to lose its second engagement with the European/American Allies, Soviet soldiers go back in time to kill Einstein. When they come home they find that the USSR is winning! Hurray! Except now because the Allies and USSR were spending all their time bombing each other, neither of them saw the Japanese gaining power...
The videogame Freedom Force vs. The Third Reich. It wasn't due to any accidental meddling, but a successful attempt of a supervillain to go back in time and provide Nazi Germany with the superpower endowing Energy X, leaving the heroes to set things right.
In the Half-Life mod trilogy "Timeline", rogue scientists from Black Mesa use the dimensional portal technology to affect time travel, then go back in time to help the Nazis conquer America by helping them complete their atomic bomb and Sanger AmerikaBomber projects. Gordon Freeman is enlisted to stop or revert this.
The adventure game Time Gentlemen Please has this as the central plot. Of course, Hitler has an army of dinosaur clones. And it all started with a simple attempt to watch Magnum PI.
Parodied in Ansem Retort when Xemnas revealed that his manipulations in time moved the Nazi occult experiments from 1940 Germany to 1831 Rio de Janiero. When Red XIII asked why they didn't just go to 1940 Germany in the first place, Xemnas realizes that he made his plan unnecessarily complicated.
The Global Guardians once had to stop a mad scientist intent on going back and killing Hitler (and thereby changing the world for the worse)... and when they got back, discovered a Nazi victory. Luckily, the rules by which Time Travel worked in the setting meant that it was an alternate dimension and not a change in the timeline.
In American Dad!, Stan travels back in time in an attempt to save Christmas from secularization. Not only does he fail, he accidentally sets off a chain of events that leads to a Soviet takeover of America. (Everything gets reset back to normal at the end of the episode, though. Well, almost.)
Inverted in Freakazoid! when he half-accidentally prevents World War II. Concerned about how the present may have changed, he returns to find things like Rush Limbaugh collecting money to help the poor, a complete lack of Chevy Chase movies, working cold fusion and Sharon Stone now being a Shakespearean actress. He congratulates himself on having made the world a better place.
The downside? The Brain is now president. But YMMV on whether that's truly a downside.
In the first season finale of the Justice League animated series, the immortal villain Vandal Savage sends information, including how the rest of the war was supposed to play out and plans for technology that wouldn't have been developed for another couple decades, to his past self in order to help the Germans win.