I would argue that the Norman conquest fundamentally changed the nature of English – and world – history. The subsequent infusion of Norman – over Germanic and Danish – law and customs had an absolutely profound effect on the character of the English, who went on to a period of world domination, peaking in the 1750s and subsequently achieved by proxy through the U.S.
The battle of Hastings has been said to be lost when King Harold was killed in 1066. It's also been said that a chance arrow shot him in the eye.
If that hadn’t happened, would the Norman invasion have failed? Opinion varies. Yet history is largely written by the victors...
It was Harold's bad fortune to face two significant invaders in the one year. He successfully fought off the Vikings to the north, only to lose to the Normans who, as it happens, were Vikings who had only settled in that area in the previous century.
Could Harold’s army have staved off the Normans if it wasn’t for that arrow?
Maybe a more pertinent question is: did he definitely die that way?
The sources I have seen do vary. In fact the chief source of the "arrow in the eye" seems to be the Bayeux Tapestry, which is subject to interpretation on Harold’s death anyway. Careful analysis yields two possible deaths depicted, including being killed by a horseman. However, the arrow could actually be interpreted as symbolic. In medieval symbolism, liars get a weapon in the eye - and Harold apparently recanted on his promise to support William's claim to the throne. (In fact, William could lay hereditic claim to the throne as the cousin of Harold's predecessor, Edward the Confessor; whereas Harold was simply son of the Earl of Wessex. Harold, however, was anointed king by Edward, then subsequently by assembly.)
If the arrow story was literal, I would argue that this would be the smallest incident that had the biggest effect on world history.
A very interesting point - raised by Mark Maddison. Comments welcome.