Saw: The Shocking Truth

The "Saw" movie franchise was inspired by a century-plus old case; in the late 1800s, H.H. Holmes began his criminal career by stealing cadavers in medical school; he would mutilate them and then make fraudulent insurance claims on them.
A Nightmare on Elm Street
S2 E8

The film "A Nightmare on Elm Street" was inspired by real cases of men who were having such terrifying nightmares, that they never woke up.

Close Encounters of the Third Kind
S2 E11

The film "Close Encounters of the Third Kind" was inspired by claims of life beyond Earth.