I have never heard of someone becoming possessed as a result of watching horror movies. I have, however, heard of a number of cases of people who are already experiencing some demonic harassment (an oppression, for example) who developed more problems after seeing the movie, The Exorcist. That one in particular really seems to stir demons up.
When it comes to movies, books, or any entertainment, I think its wise to live by the standard St. Paul set forth in Philippians 4:8 -
Finally, brothers, whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is gracious, if there is any excellence and if there is anything worthy of praise, think about these things.
If what you’re viewing doesn’t pass this test, it’s probably not worth watching.