The Amityville Horror is based on the alleged haunting of a house in Amityville, New York, while The Conjuring is based on the experiences of paranormal investigators Ed and Lorraine Warren, who were involved in the Amityville case as well as many other famous paranormal investigations.
The most famous horror film based on a true story, however, is the 1979 fearfest, The Amityville Horror. The movie was so popular that it inspired a franchise of forgettable sequels, and even a Ryan Reynolds-led remake in 2005, but none could match the impact of the original.