Narrative Conventions

Thriller can be split into a few sub-genres, the key ones being: crime, mystery and psychological. These are the key narrative events that happen in these films for each sub-genre.
Crime: ransoms, captivities, heists, revenge and kidnappings
Mystery: investigations,'whodunit technique', police
Psychological: mind games, psychological themes, stalking, confinement, death-traps,horror of personality, obsession

The conventions of crime are evident in the narratives in the Dark Knight. For example, beginning when the joker robs the bank and also in Taken when the main protagonists daughter gets kidnapped. 
Shutter Island uses the narrative conventions of mystery in Shutter Island by having a police investigation as the main point of the storyline. 
Psychological games are used throughout the narrative in Seven. 
Most thrillers involve a set up based around a certain crime, this is an old convention from when thriller films started off.

The narratives are always used to thrill the audience, hence the name of the genre. Usually the main protagonists life is put at stake. This makes it more thrilling and exciting because the audience have formed an attachment to the leading character and strive for them to survive.

Most narratives are tense, this keeps the audience on the edge and allows them to be thrilled more effectively because they know something potentially bad, yet exciting will happen.