The suspense movie is a classic part of the movie tradition. Some of it's origins are in Film Noir and many consider LA Confidential to be a Suspense Movie. Suspense is a genre that almost never veers into the supernatural. It usually involves a relationship. The Player is another film that you wouldn't expect is also considered a part of the suspense genre. Body Heat, Basic Instinct, and Fatal Attraction are more traditional films within the supsense genre.
The trademark suspense genre film is this: Boy meets girl. Boy and girl have a love scene in the first 30 minutes of the movie(if they don't have a love scene in the first 30 minutes usually the film opens with a love scene to keep people intrigued). Boy and Girl break up and then Girl makes things complicated for boy... Many people hate the third act of the movie. They call this third act the bunny boiler third act. They want the third act to deal more with social situations that were more in tune with why the enjoyed the first two thirds of the movie. Chloe a suspense film has an intriguing solution to this that involves abbreviating the bunny boiler portion of the film to a swift five minutes at the end. Orphan is an example of a good suspense movie that becomes too bunny boiler at the beginning and end of the film.
The key ingredient to a suspense film is the love scene. Even in a made for TV movie suspense film you have to have the love scene. Then there are other supplementary ingredients. You have to have the grace period where the characters are just working at their jobs with no idea of the intrigue that awaits them. You have to have the passion between the boy and the girl. Teases as to when they will finally consumate their forbidden relationship.
Then you have to have the mystery. Does the girl have a mysterious past or is the boy a part of a secret dark organization? Then there's the bunny boiler part of the movie that people hate. How do we write a script that avoids this? Really, what the bunner boiler section boils down too is a confrontation between the characters. The girl doesn't have to kidnap the boy's child. The boy and girl just have to confront each other. Maybe the boy lays a trap to trick the girl into meeting him at a psychiatrist's office. Maybe the boy confronts the girl at a public place.
Then there's the twist ending. In Roger Ebert's review of the Usual Suspects, he stated that the twist ending came out of nowhere and disliked the film because of that. I think that the twist ending doesn't have to make any sense whatsoever with the rest of the move. If there's no big twist ending then I feel cheated. I see suspense film twist endings as a competition to outdo other suspense films. If there's no twist ending, the film makers just aren't competing. I don't care if the twist ending is "it was all a dream" or "it was an experiment by aliens". Having a suspense film without a twist ending is like having a sundae with only the cherry but no ice cream.
A suspense film is a relatively formulaic picture type that relies heavily on the dynamic between the characters, the strength of the love scene, and the brilliance of the twist ending. If you combine all these elements you will make a successful suspense film.