This movie is genuinely attempting to be a horror film, and is promoted as such; further, the time travel elements are integral to the horror--it is the terror of being trapped in a time loop.  In response to our original analysis one correspondent suggested that it was not a time travel movie at all, but that the main character Jessie has been condemned to hell, and this is her personal eternal punishment.  While that is a viable interpretation of this movie, which is replete with horror tropes and a bit gory, if we accept that view it ceases to belong here with the time travel movies at all.  It was not what I would call an enjoyable movie, and it was certainly a horror in terms of its time travel, but it does get good marks for making the effort to use a Bermuda Triangle-like scenario temporal loop as a horror setting.  We analyze it here.

This was one of those movies that time travel fans talked about, raving about how complex it was.  It proved to be temporally rather simple, although the solution required accepting a few theories concerning its supernatural realm.  We don't realize that the apparition in the rabbit costume is the ghost of someone the main character is going to kill, but we watch as the spirit leads the person through a disastrous life to the point where the shooting occurs.  It was fairly well done, as long as you ignore the Internet book that supposedly is the book in the story, which was written well after the movie was released and only confuses matters.  We did an analysis on the original site.

The sequel, S. Darko, is more eerie than anything else.  Our analysis (also here) found many problems, including people who will not die if they die.  It was an interesting and in its own way much-anticipated sequel, but did not live up to the original on any level.  The presence of ghosts and conversations with the departed puts this in the supernatural realm, but it is never really terribly frightening despite the several deaths.

Unlike its two prequels, this has the feel of a thriller from its opening scenes.  The main characters in the first two films discover that they can travel to moments in their own past by using reminders of times and places where they were, and manage to complicate their lives trying to make them better.  Our central character here, unrelated to those, has refined the ability significantly, and uses it to visit murders, returning to the present where he pretends to be a psychic who sees visions, and collects reward money for providing information that leads to an arrest in these unsolved crimes.  Things get complicated when he starts trying to solve the murder of his own high school girlfriend, when the girl's sister persuades him that the wrong person was arrested.  The noose tightens around him because he is working against another time traveler who manages to stay one step ahead of him until he is arrested for a murder and does not know who did it.  Find the full analysis here.

This was a brilliant time travel story in which a man wanders into the woods in pursuit of a girl he glimpsed through the trees, and winds up chased by a masked man, and then hides in an experimental time machine.  It is a complex story in which we wonder at times who died and who was the killer, and in the end someone is dead and the killer seems never to have existed.  It is a Spanish film which is available subbed and dubbed in English; there was talk of doing an American remake, which we are still hoping to see, and hoping that the Americanization of the script does not destroy what proved to be a wonderfully intricate and workable time travel plot.  It ranks high on the list of well done time travel stories, although its moderate budget shows in places and as a thriller it is not as compelling as our remaining two.  Our analysis is here.

Sometimes when there is a fatal accident it absolutely shatters your life.  In Premonition (analysis here), that happens to Sandra Bullock's Linda in a major way:  her husband is killed in a car accident and she lives an entire week out of sequence, on some days of which her husband is alive and on others dead.  The viewer joins her in trying to grasp what has happened as she goes from attending his funeral to discussing his business trip, and we feel it pulling inexorably toward the fatal accident from which it all began.  It is thought-provoking and disorienting and eerie, and not a little frightening along the way.  Despite major temporal problems, it is a significant and worthwhile time travel film.

Although the sequels became great action-adventure films, there is no doubt that the original Terminator movie (our original analysis of which is still here) was a horror film, built on many of the genre tropes.  It has a monster that seems invulnerable, a threatened helpless girl who becomes the hero, a hero who dies protecting her.  Several times when we think the monster is dead it suddenly rises and attacks again.  It also uses the tricks of making us expect a surprise attack, relieving the tension with a fake, and then abruptly bringing the anticipated attack from a different direction.  Everything about it screams "horror movie", and it is one of those films I would not have watched had it not also been a great science fiction film and a good time travel movie.  It is argued that the first movie is a fixed time story, but the second clearly is not, and the first does not have to be.  It is good enough to be worth being a bit frightened.

Those are the best time travel thrillers I've seen, and some that are maybe not so good.  If I missed one, let me know--it is possible I have not seen it, and I should analyze it when I can.