I've heard people categorize it as a horror film, art film, thriller, even a black comedy. Which is it? Even my Film Studies professor was unsure.
According to Wikipedia, it's considered a horror film.
The Shining is a 1980 horror film produced and directed by Stanley Kubrick and co-written with novelist Diane Johnson. The film is based on Stephen King's 1977 novel The Shining. https://en.wikipedia.org/wiki/The_Shining_(film)
However, many consider the film a psychological-thriller or psychological horror film...
The Shining - A psychological thriller The Shining relates in many ways to other psychological thrillers. A psychological thriller is a sub genre of a thriller whereby the director uses elements that relates to the mind or the processes of the mind. They are mental rather than physical in nature. The main characters are usually more reliant on mental resources instead of physical strength to overcome their issues. There are many different conventions featured in “The Shining” that relate to the thriller genre and help make the film a more tense and suspense filled great. A film that is extremely disturbing but yet compels the viewer to see more. Kubrick made sure that this film would be perfect in all respects and made no mistakes. He understood how to capture the audience and how to really disturb them with chilling and menacing moments. The whole film including the camera movement, shots, angles and sounds all combined together with such perfection that the audience is completely inhaled in the intense, exhilarating madness that is “The Shining”. http://conventionsthriller.blogspot.com/2011/10/shining-psychological-thriller.html
To understand how hard that is, watch another psychological horror film that’s very good—and then compare it to The Shining. For example, take The Vanishing—the 1988 Dutch original, not the crappy American remake. It’s a measured, smart, offhandedly creepy, absorbing film. On Rotten Tomatoes, it’s 100% fresh. Still, do you care about these characters as much as you care about Shelley Duvall and her young son in The Shining? No.
What makes The Shining work so well is how adeptly and efficiently Kubrick and co-writer Diane Johnson draw us into King’s narrative of domestic violence. Even as Jack Nicholson is touring the hotel, we’re being given hints that there’s a deep tension in the couple’s relationship. After the family move in, the story simultaneously and insidiously advances on both the supernatural and psychological fronts: we learn more about the family’s history just as we’re learning more about the hotel’s history. http://thetangential.com/2014/10/27/why-the-shining-is-the-best-psychological-horror-film-ever/
Just to add, even the though the film holds it's own weight and does not explain or better examine it's mythology like the book does, I would also argue since a lot of Stephen King works tie into The Dark Tower series, that one could make an argument that The Shinning (and it's sequel Doctor Sleep) have supernatural elements as well, lending itself to science-fiction & fantasy also.