Change in Language
One major impact from the Battle of Hastings that can still be seen today is the change in the English Language. William being from 11th Century Normandy, spoke French, and when he conquered England he brought the Norman / French language across with him. In fact, after the invasion of William the Conqueror, the next king of England to speak English as their first language was Henry IV, more than 300 years later!
In the court, an Anglo-Norman language was used, but for the majority of the Anglo population they continued to speak their English. Eventually over time, the two languages merged together and created a new one.
Often the difference in language was associated with a difference in class / working / society. This can be seen in jobs and trades of the time - with trades like bakers and shoemakers keeping their Anglo-Saxon names, whilst trades such as a tailor or merchant adopted the French name.
The clearest difference is with food - most farmers would have been Anglo, so the names of animals stayed the same, such as cow, sheep, deer. However, once served and ready to be eaten their names became French, beef, pork, bacon and venison...