1066 itself is a year much written about, as it saw three battles of importance in English history
The most famous of the battles was the Battle of Hastings, or Senlac Hill, in which the invading army of William Duke of Normandy finally defeated the Anglo-Saxon defenders of King Harold Godwinson, who died in the battle, allowing William to become King William I of England. (From Battles of the Medieval World)
The battle was pretty much a wash for much of the day, Norman cavalry charges against an Anglo-Saxon shield wall on a hilltop gaining neither side much (not even many deaths) until a second false retreat lured the Anglo-Saxons into breaking their wall, which began their defeat. The importance of archery in the battle is debated, but one arrow at least counted greatly– the one that struck King Harold Godwinson in the eye and lead to his death, which finally broke the Anglo-Saxons. The scene is depicted in the famous Bayeux Tapestry, a near 230 foot cloth illustrating events around the Norman Conquest of England. (From The Medieval World at War)
The role played by archery is surely not that much in doubt – but the archers alone didn’t win the battle for Duke William. They certainly created the gaps in the shield wall – gaps which could then be exploited by the Norman cavalry as the battle drew to a close.