What if: Alexander makes peace with Darius, getting the Persian Empire up to the Euphrates, one of Darius' daughters in marriage, and an alliance [Parmenion urged him to do so]. Alexander had already declared Carthage his enemy. Would Alexander have then moved into the Western Mediterranean? There were Greek cites along the littoral, and on Sicily he would have wanted. And would Rome, the mother society of all western culture have survived?
Hannibal wins the Second Punic War, leaving Carthage, not Rome, the dominant power in the West.
Mongke Qua Quan doesn't die on campaign in Sung China, leaving his brother Hulegu with his whole Army for the invasion of Egypt, and the potential destruction of Muslim power in the Middle East.
The Emperor of Byzantium pays the artillery designer who built the guns Mahmet used to bring down the walls of Constantinople for the guns and his services [which were offered to Byzantium first].
English Major Patrick Ferguson forgets about chivalry, and kills, with his rifle, the American officer he sees riding across the river [or stream] from Ferguson's location, the officer being George Washington.
England declares war on the United States after the Trent Affair, allying with the Confederacy.
Anybody care to add to the list? Discuss the ones posted above?