I have read the books about some of their higher-profile cases---
The Amityville Horror; and
The Haunting (dealing with the Smurl family case in Pennsylvania), and the cases of the Perron family in Rhode Island (made into the movie
The Conjuring), the Snedeker house (made into the movie
A Haunting in Connecticut), the Hodgson case in Enfield, London (made into the movie
The Conjuring 2).
I didn't find anything in them to fit in with the attacks their critics have plastered them with; I think a lot of it is simply attacking anything of this sort by people who stubbornly refuse to accept that there's anything supernatural in the world, similar to the people who debunk UFO accounts or people who slam Creationists or Catastrophists because their views disagree with evolution and uniformitarianism.
There is a documentary out there called
My Amityville Horror, released in 2012; Danny Lutz, the oldest son in the case, recounts his personal experiences in the house, and their aftermath; Lorraine Warren is also in the film. They both make a very, very convincing case for their truthfulness and sincerity, in my humble opinion. It's worth a watch, but be warned: Danny uses some pretty gritty language throughout the film. Nothing you wouldn't hear on a military base, but it's there, so just be aware if you decide to watch it.
