Psychological:
A deaf woman is stalked by a serial killer who believes she is the perfect victim, but she strikes back and starts to hunt him. Mild gore, but more thrilling.
A woman escapes her abusive husband, only to be stalked by an invisible foe.
A woman (apparently I need to start every entry like that) is killed by a motel owner, her sister and her lover try to find her.
Notable mentions: Psycho 2 and Psycho 4, but not Psycho 3, which sucks harder than a ladybug sucks on an aphid.
After a one-night stand, a traveling photographer is locked in the apartment of her lover, and he keeps her hostage.
Julia's blind twin sister commits suicide. She travels to the city and stays, only to be stalked by a mysterious man. Not helped by having the same genetic illness her sister had, and quickly going blind.
Paranormal:
A family moves into a haunted house, and Ed and Lorraine Warren need to save them.
A boy gets a Good Guy-doll gifted for his birthday, murders start to happen around him.
A jackal in a zoo delivers a human baby, it is quickly replaced with the baby of a politician, and little Damian will do Damian things.
Honorable mention: Omen 2, but not Omen 3.
A woman and her husband move into a new apartment, he quickly becomes friends with the eccentric neighbors, and she nearly loses her mind.
A traveling merchant picks a rose in a beautiful garden. A beast appears and asks for his daughter as a punishment for stealing from him.
Edit: Somehow The Frighteners got deleted.
Michael J Fox sees ghosts, has a successful business in swindling people to get rid of ghosts, finally has to get rid of a murderous ghost.