Basic Information
This Time Travel Trope refers to the concept, popular in fiction and sci-fi media, that something horrible and epic (aka WWII and/or The Holocaust) must happen between the years 1930 and 1947, and it's unavoidable. No matter what you do, you just can't win. It doesn't matter if you go back and try to kill Adolf Hitler. You'll fail at the attempt. Or you'll succeed, but the Nazis will still come to power, and maybe even win the war now that Hitler's not around to make various leadership mistakes. Or you'll succeed, but it turns out Adolf was secretly adopted when the first-born son of the Hitler family was murdered as an infant, meaning you killed the wrong baby. Etc. You're doomed to fail.
For those who insist on trying anyway, Hitler was born on April 20, 1889. Have at him - the bastard deserves whatever hell you can give him… unless all those attempts on his life by various time-travelers are what lead directly to his being a paranoid, bigoted, power-grabbing, murderously genocidal, megalomaniacal fiend in the first place? …Nah, he still deserves it. Just be wary about Godwin's Law of Time-Travel.
Should you feel the need to drag science into this, the mechanics behind Hitler's Time-Travel Exemption Act can be explained by the Novikov Self-Consistency Principle or possibly the Chronology Protection Conjecture.
Sources
Game and Story Use
Approaching this subject in a game requires some forethought. Players who set their sights on stopping the Holocaust are likely to be very determined, and won't give up easily. You also have to be careful or you might accidentally absolve Hitler of the murder of millions, or imply that God is protecting Hitler, either of which would be rather distasteful (not to mention insulting to the memory of his victims). Proceed with caution, and know your players well.
- Perhaps Hitler is just the latest in a long series of rewritten horrors in the era. There could be a time traveling character that keeps going back and killing or suppressing various dictators and madmen in the 30s and 40s. Maybe every time he tried to fix things, the situation just got worse. Perhaps after the 12th or 20th alteration that had backfired, he decided to leave it with his latest version of the disastrous decade, which is the history the PCs have grown up in. At least in this version, the Nazis eventually lost.
- In a setting with Time Police, there could be a unit dedicated to preventing meddling with this era. It's no doubt a favorite target of time travelers from later eras, so they'd find themselves very busy. This would result in some serious moral ambiguity - the Time Police are generally regarded as good, but this unit actively protects one of histories greatest villains.
- In a setting where the Universe itself somehow prevents alterations of the time line, killing Hitler could become a rite of passage for Time Travelers. Perhaps several hundred time masters have killed Hitler at this point, and the Universe responds with ever more implausible circumstances to keep WWII on track.
- In a game with not only time travel, but also magic and the supernatural, Hitler could be some sort of undead or other unkillable evil. Time travelers keep trying to whack him, and he just dodges every attempt. Be careful not to accidentally absolve humanity of it's guilt and complicity. Giving the Hitler-Lich the ability to control the actions of large crowds via powerful magic would probably be a bad idea, since it turns the members of the Nazi party into victims instead of perpetrators.