Answer:
An American Crime, Stuck, Open Water, Train, The Mothman Prophecies, The Amityville Horror, The Haunting in Connecticut, The Exorcist, The Exorcism of Emily Rose...
However, you should be aware that some of these movies (namely, The Amityville Horror, The Haunting in Connecticut and The Exorcist) are at best very loosely based on the real thing, and at the worst, a scam/hoax.
You should also be aware that a lot of movies -- namely The Strangers, Hostel, Wolf Creek, The Texas Chainsaw Massacre -- claim to be "based on a true story" or "inspired by a true story" when in fact they are essentially entirely fictional. Movie producers and marketers in Hollywood know that people are more likely to see a horror film if they think it's based on a true story. So they love to label movies "based on a true story" or "inspired by a true story," even when it's not really true.
None of the events depicted in the films listed above -- The Strangers, Hostel, Wolf Creek, The Texas Chainsaw Massacre -- ever happened in real life. All the characters are entirely fictional, and none of the events depicted ever took place. None of these films were intended to depict any true occurrences.
For example, the "real story" behind the Texas Chainsaw Massacre didn't happen in Texas, didn't happen with a chainsaw, and wasn't a massacre. The writer/director of The Strangers got the idea from several different true crime cases...none of which resemble the characters and events in the movie to even the slightest degree.
Wolf Creek was written as an entirely fictional story. It was only AFTER writing the screenplay that the writer/director discovered that his story vaguely resembled some true crime cases that took place in Australia. So he edited the screenplay slightly, so it would resemble the real cases a bit more, and when the film came out, it was labeled "based on a true story."
And Eli Roth got the idea for the Hostel movies from a website that a friend showed him, advertising a "murder vacation" in Thailand, where, for $10,000, you could shoot someone in the head. He doesn't even know if the website was a hoax or not! But again, the Hostel movies are labeled "based on" or "inspired by a true story."