As I'm sure some of you are no doubt thinking, its fair to say that The Terminator isn't exactly a horror movie in the classical sense, as it's somewhat short on much of the traditional imagery associated with the genre. It's also understandable that the film is more commonly pegged as a science fiction thriller, due to the whole time-travelling cyborg assassin business. However, the more one considers the basic dynamics of the story and the overall mood/effect generated by all the varying elements, the more it becomes apparent that it actually contains as much of the quintessence of the horror movie as almost any other superlative example of the genre.
This is another one of those films where a synopsis seems frankly superfluous, although I suppose it's worth saying a little bit about the genesis of the general idea behind it. The image of the Terminator itself apparently came to Cameron in the delirium of a fever dream, and its now iconic, mechanical death's head is certainly a potent, nightmarish image; a post-apocalyptic memento mori, if you will. Other story elements are admittedly influenced by a couple of Harlan Ellison scripted Outer Limits episodes; "Soldier" and "Demon with a Glass Hand".
The main thing which arguably makes The Terminator a horror movie is its portrayal of an impersonal, unstoppable, and seemingly indestructible killing machine that is completely, and single-mindedly committed to its purpose, which is, to annihilate yo' ass. When all is said and done, Michael Myers and the T-800 aren't that different, it's merely their motives that vary. In fact, Halloween (not to mention many other slasher films by proxy) and The Terminator are actually quite similar in the way they plot their general narrative trajectory. This time it's Uzi 9mm toting, time travelling robots that the protagonists have to worry about, as opposed to amoral, immortal, sister-obsessed psychos, but essentially, the story plays out in an analogous fashion. In both films, the killer has one woman in mind as its central quarry, but initially ends up chalking up a fair amount of collateral damage, so to speak, to get to her. In this context, Sarah Connor is obviously the proverbial Final Girl then.
Other elements that help nudge the movie even further into horror territory include its midnight movie, city-that-never-sleeps, neo-noir ambience (come to think of it, the name of the club that Sarah hides out in at one point, 'Tech Noir', sort of sums up the general aesthetic) and the often doomy, driving, and now iconic, synth-laden score, composed by Brad Fiedel. There's also a cheeky false scare featuring an animal (an iguana this time) and bit of that old chestnut beloved of the surrealists and Lucio Fulci: eye violence. What more do you want from a horror film?