“If you were given the power to travel through time and Set Right What Once Went Wrong, what would you do to prevent the atrocities of the past? Well, for many, the answer is obvious: kill Adolf Hitler. This would prevent World War II, the Holocaust, and their myriad side-effects… right?
Unfortunately, it doesn’t seem to work that way.

“First of all, it often proves near-impossible to kill the man in the first place — like most dictators he’s protected by various bodyguards and security forces. After all, the guy survived about 42 real life assassination attempts. Trying to circumvent these by targeting him before his rise to power begins will usually turn out to be ludicrously difficult as well. Locating a lone, disillusioned war veteran wandering around post-WWI Europe is perhaps the ultimate needle-in-a-haystack search. And secondly, even if you do manage to kill him, something even worse will appear in his place; an even smarter and crueler Führer who wins the war for the Axis, or an individual killed in battle instead grows up to terrorize the world, assuming Josef Stalin doesn’t take advantage of the fact that Germany isn’t invading Russia in this new timeline and its the Soviet Union that starts World War II this time. If someone actually does stop Hitler, they’ll almost always have to undo it to prevent this…”

Examples:

– In Stephen Fry’s 1997 novel Making History, Hitler’s parents are prevented from conceiving, but his absence allows the taller, more handsome, cleverer Rudolf Gloder to ride the tide of frustration that gave birth to the Nazi party, and the results of his reign are worse for the world than Hitler’s. Gloder has negotiated a stop to the war with Germany still in control of most of its conquests, and has reined in the anti-Semitism to the point that it hasn’t inspired total war from his adversaries.

– A passing mention of this is made in Robert A. Heinlein’s The Cat Who Walks Through Walls. The plot involves an agency that can travel through time and across parallel universes. One of their early attempts at improving the world involved assassinating (humanely, they simply ensured that his parents were using birth control on the day of his conception) a Hitler-like dictator. His brutal reign doesn’t happen, but what was originally a small-scale nuclear war turned into a global one, since the Hitler-analogue had kept the alternate America out of the war. They rid the world of the evil dictatorship, sure, but they also rid it of all life other than cockroaches. Unusually for this trope, they didn’t take their failure as a sign that there are things they shouldn’t be messing with; instead, they decided they needed better projections about what would happen should they make a change.

– The Iron Dream is a rather unusual example set in an Alternate History where Hitler emigrated to the US after World War I to become a Sci-Fi/fantasy author. In this world, the Soviet Union conquers all of Eurasia and Africa. But this is all background material— Norman Spinrad instead uses Hitler’s book-within-the-book The Lord of the Swastika to point out the Unfortunate Implications of Golden Age militaristic SF.

– Connie Willis’s time-travelling historians can’t go back to any event which is over a certain threshold of “significance” to world history. “The net” (the name for their time machine) won’t open for them, or if it will, results are unpredictable. In-universe, someone did once try to go to Germany to kill Hitler in the early days of the net and ended up in South America. Similarly, you can’t go to Waterloo or Lincoln’s assassination. Since historians can be in the past for extended periods and travel freely once there, it’s never explained why you can’t go to a different location a bit earlier and travel to the site of the event you’re interested in (perhaps the net somehow knows what you’re up to?) but then it’s never really explained why it’s lethal to exist in the same time period twice, either.)

Text: Hitler’s Time Travel Exemption Act, TV Tropes.com

Image: Extract from Operation Foxley briefing, UK National Archives Education Kit.