AlternateHistory is a SpeculativeFiction subgenre that posits what would happen had some particular event in history turned out differently than it did. There are many of these "Turning points" in history, like the Battle of Marathon, the D-Day invasion, about a half-dozen battles in the American Civil War, etc. This is also the branch of literature that deals with questions like "What if Hitler had never been born?"
HarryTurtledove is probably the acknowledged master of this genre, with several series of books that masterfully play this "What if" game. His book GunsOfTheSouth? is both good fiction and an excellent analysis of the political and military history of the period. However, HarryHarrison? and SmStirling? also have contributed excellent books in this genre. Nearly every ScienceFiction author has at least tried to write a short story or novel in this genre, some with more success than others. For instance, AllenSteele?'s "The Tranquility Alternative" is a great examination of what might have happened had Von Braun's plans for the U.S. space program described in Collier's had literally come true as he outlined. However, if you examine any of the many collections of short stories by ScienceFiction authors that MartinGreenberg? has edited (like "Alternate Generals" and "Alternate Americas") you'll see that it's not at all easy to avoid making the story just a thin shell around a lame McGuffin.
This kind of novel has recently began to show up as mainstream fiction. For instance, RobertHarris?' book Fatherland is written with the assumption that Hitler won the second world war, and is written from the perspective of a detective who stumbles upon the truth behind all of the Jews who "went East".
Lately, this kind of "What if" game has taken on a life of its own among historians, who call this kind of analysis a "Contrafactual". Examples include "What If? The World's foremost military historians imagine what might have been" and "The Hitler Options: Alternate Decisions of World War II".
See CivilizationGame