Basic Trope: "The first rule of time travel is that any and all modifications made to the timeline result in Hitler winning World War II."
Straight: Bobby McTrope has a thirst for adventure and is too lazy toreadhis history book in order to write an essay for school. Knowing that his new neighbor is a Mad Scientist with a Spacetime-Traversing Pogo Stick, Bobby steals it and hops into the past. He ends up in Austria in 1905 and meets a nice, artistic young man named "Adolf". When Bobby leaves and goes back to his own time, he discovers that Those Wacky Nazis won WWII and conquered the world because Bobby left his history book in the past and his friend Adolf used it as a user's guide to dictatorship.
Exaggerated: Bobby McTrope leaves his history book in the past, but flubs up his return to his own time and ends up several centuries in the future. In the year 2589 not only are the Nazis conquerors of the world, but they've claimed the whole galaxy as part of the Third Reich. And Hitler is still alive!!
Downplayed: On his return trip Bobby finds out that the Nazi Party is still active, still runs Germany, and has conquered most of Western Europe.
Bobby McTrope is a Neo-Nazi and intentionally goes back to help Hitler win the war.
Bobby never learned the rules of time travel.
Hitler tricks Bobby McTrope into giving him the Spacetime-Traversing Pogo Stick and then uses it to go to the future and try to conquer the world.
Bobby goes to the past and accidentally leaves his history book where President Roosevelt can find it. He comes home to find that America has conquered the world!
Bobby McTrope's interference in the past ends up causing the Nazi Party to quickly collapse and never gain the infamy it has today. Wikipedia's article on Hitler is nonexistent.
Bobby McTrope's interference in the past ends up making the Soviets "win" the Cold War.
Bobby is a Neo-Nazi who purposely tries to manipulate the past so that Hitler wins World War II. He gets increasingly frustrated when his attempts never work.
Subverted: Bobby McTrope leaves his history book in the past with Adolf Hitler, but after reading the book, Hitler, disgusted to learn of the crimes he will commit in the original timeline, actively goes out of his way not to become a dictator. Hitler lives an average life without any notoriety, whether good or bad, and dies after a very long, fulfilling life.
Double Subverted: Although Hitler led an unassuming life, another German, Victor der Nacht, rose in power and formed a fascist political party known as the Nazis. He was a more charismatic, more strategically adept leader and general than Hitler ever could be and he conquered the world.
Bobby takes the Spacetime-Traversing Pogo Stick back in time just one week, and spends his extra time swimming with a girl in Fiji. When he returns, the German Empire won World War I.
Bobby altered an event in 1960, resulting in the Nazis winning World War II, despite the fact that the war finished 15 years earlier.
Bobby goes back to a barren wasteland in 1938, stays there for five seconds, then departs after saying "This is so boring and useless. I'm going back to my own time." He leaves no apparent trace of having ever stood where he so briefly did. When he returns to the present, Hitler has won WWII.
Some random alterations to the timeline will cause Germany to win WWII, while others will cause the Nazi Party never to gain power.
Bobby McTrope goes home after leaving his book lying around, but the young Hitler loses it before he can read it. It travels around Austria and Germany for fifteen years before it falls into the hands of an older, seasoned anti-Semitic German politician — who believes its entire contents are worthless fiction and throws it away.
Averted: Bobby McTrope goes back in time and on the return trip everything is exactly as he left.
Lampshaded: "I went back in time and accidentally gave Hitler what he needs to win World War II! Everything else is pretty much the same, though..."
Invoked: God set off the Big Bang and decreed that if any of His creations should travel back in time and alter what was written, "The inverse outcome shall arise."
Exploited: Realizing that Bobby is from the future, Hitler tricks him into giving information about the future.
Defied: The time traveller knows exactly how to change the past without accidentally aiding the Nazis.
Discussed: "I don't even know what could go wrong if I just looked around Vienna in the first decade of the 20th century...oh, right, he lives here."
Conversed: "At least Bobby Got Back was historically-inspired fiction. Some people need a good scare like that to comprehend how easily a Crapsack World could have arisen from the ashes of The Forties."
Bobby comes home to find his teacher speaking to his parents about his academic lassitude; she addresses them, however, as "Mr. and Mrs. Tropelhaus" rather than "Mr. and Mrs. McTrope".
Bobby goes back to bed immediately upon coming home. When he wakes up, his father is standing over him sporting Hitler's trademark toothbrush moustache and tries to Hand Wave this by explaining "It's been in fashion for decades, Bobby!"
Deconstructed: Even when time travel actively aids them, the Nazis cannot win the war because of all the internal issues of Nazi Germany, and by their own racism. Giving them technology is pointless because they don't have factories or the materials to make it. Even if you do, you run into the problem of the several and often competing science groups, while also not being able to bring back which requires and understanding of science revolutionized by Jewish scientists (including Albert Einstein). Future battle plans may save them in the short term but will quickly become useless as failed battles and campaigns lead entirely different battle plans and campaigns. Assassination attempts using information on political leaders real locations, since most of the various (also constantly in fighting) German spy agencies are working for the Allies. All anyone can do is extend the war, with a constant struggle against the Reds with Rockets in the Ural Mountains until the U.S. can start bringing in their "final solution".
Played For Laughs: Bobby's meddling caused Grammar Nazis, not true Nazis, to take over the world.
Played For Drama:
Those selfsame Grammar Nazis, though ostensibly innocuous, immediately ostracize Bobby because their official government policy discourages his scholastic ineptitude.
As soon as Bobby crosses the threshold over 1941, he feels himself beginning to be erased from existence because his great-grandfather was killed at Pearl Harbor before fathering Bobby's grandfather, thereby also eliminating his mother and, through her, himself.