No, it's doesn't look as though Ouija was based on a true story. At least, that's the official line by the movie companies who promoted the film. They say that the movie is based purely on the Hasbroboard game of the same name.
I am quite relieved to hear this to be honest, as it looks terrifying! Even the tag line "Keep telling yourself it's just a game..." gives me the creeps.
Whilst this movie may not be based on something that actually happened, there are some super scary "real-life" ouija stories around. Check out this Thought Catalogue piece by Chrissy Stockton. Number 3, "Creepy Doll", is particularly disturbing...
Here's a trailer for the movie. You might want to watch it with the lights on! The movie stars Olivia Cook, an English actress who also starred in Bates Motel, (a show based on the equally creepy film Psycho) where she plays Emma, the friend of a young Norman Bates.