It seems no story of time travel can exist today without mentioning the idea of going back in time and killing Hitler, which sounds like a good idea even though it's one mighty big butterfly to step on.
The theory has evolved to killing Baby Hitler, thereby eliminating the Nazi era from even happening and possibly preventing World War II altogether.
But this creates a new conundrum- could you kill a cute little baby, even if that baby would grow up to be one of the most notorious figures of the 20th century?
Jeb Bush recently said he'd have no problem killing Baby Hitler (actually, he responded to the question with an enthusiastic "Hell Yeah I Would!), but he's not a very good example of normal human morality.
Personally I think the time traveler vs. Hitler debate could be solved without any bloodshed by going back in time and buying Hitler's paintings, thereby legitimizing his art career.
Hitler the artist will be too busy drawing Disney characters and painting portraits of German Shepherds to bring the Nazi party to power, and thirty years later we'd spot him hanging out with Andy Warhol in SoHo!
-Via Know Your Meme
One amusing theory along these lines is that it has been tried (it will be tried? it was tried? time travel grammar...) by dozens of time travelers already, and that we have records of many of the failed attempts listed in the "Assassination attempts on Adolf Hitler" Wikipedia article. It wouldn't surprise me if some attempts that happened before 1934 have been left out of the records, including possible baby Hitler attempts.