Alexander the Great, King of Macedonia, tried to conquer the whole of the Western world. He had succeeded in the Persian Empire and was planning to move into Arabia and then west onto Carthage and Rome. Instead, fate struck and he died suddenly aged only 32 in 323BC. He left a Greek-speaking Middle East, but the Roman Empire developed to the West. Had he lived, the whole of the Western world would be Greek-speaking.
In 1714, the United Kingdom Parliament elected George of Hanover, a German prince, as king. The next year there was a Jacobite insurrection in support of the rightful claimant to the throne, James the Old Pretender. The rebels took most of Scotland and part of England. They had been promised French military assistance. Then fate struck: King Louis XIV died leaving his six year old great-grandson as the new King of France. The Regency decided not to send soldiers to assist the Jacobites, and their rebellion therefore failed. Britain retained the liberal Protestant Hanoverian dynasty instead of an authoritarian Catholic Jacobite one.
As German dictator (1933-45), Hitler survived thirteen serious assassination attempts. If any one of them had succeeded, it would have changed the course of history because his designated successor (Marshal Goring) was much more moderate. Fate, however, decreed otherwise, as described in Luck Of The Devil: The Story Of Operation Valkyrie by Ian Kershaw.
In 1985, the Soviet leader, Konstantin Chernenko, died. The Politiburo immediately convened to elect a successor. Two members were unable to attend, they were both opponents of the liberal Gorbachev, who in their absence, was elected by one vote. Following this twist of fate, he proceeded (unwittingly) to dismantle the Soviet Union thus changing the course of world history.