Fantasy is my #1; I will give almost anything a chance if it has strong fantasy elements. Post apocalyptic, superhero, alternate history, science fantasy, some supernatural, romance, and a few fandoms (especially Game of Thrones) are also likely to catch my eye.
I've seen people put The Silence of the Lambs on lists of psychological horror movies, so probably that.
If you want to discount iffy borderline cases that are more thriller than horror, then I'd probably have to go with the first Saw movie. I don't really care for horror films in general, but Saw was pretty great because it built up a creepy vibe without needing to rely on much in the way of jump scares or blood and gore. It saved the bloody bits for the climax, and that worked just fine for me. The later Saw movies lost my interest because they were just gorefests.