This picture is from 'Die Hard 4' which would be described not only as an action film, but a thriller also as it has scenes of suspense.
Films such as 'Donnie Darko' and 'The Butterfly Effect" would be described as psychological thrillers. Not necessarily horror and not necessarily violent or rich in effects.
Certain aspects of the psych-thriller convene to the typical aspects of the thriller, such as the music, and parts that make an audience 'jump'
Some thrillers show us a central focus on a relationship, this often follows an action role, such as the movie 'Fatal Attraction'.
There are so many horror thrillers that 'horror' is its own genre, yet many of its conventions are about suspense, unexpected appearances, and false plateau. For example a film like Paranormal Activity.
Political Thrillers tend to stay away from the horror and supernatural side of things and focus on a very real issue, yet still combine the suspense of a thriller. An example would be 'Enemy Of The State' or 'Vantage Point'.
A 'Suspense Thriller' focuses solely on suspense through the whole movie, such as the movie 'Phone Booth' where there is a scenario throughout the whole film which builds up suspense and reaches a climax.
I would say my favourite is the psychological thriller, as 'Donnie Darko' and 'the Butterfly Effect' are both films i greatly enjoyed and would draw influence from in ideas for my final coursework thriller piece.