OK, I’m going to totally cheat here because I’m about to give my three non-horror movies for horror fans as well as three runners-up. I will divide them into the categories of science fiction, comedy and fantasy.
Science Fiction: Because horror so closely rides a parallel rail next to science fiction, I’ll start with that category. My pick for a non-horror sci-fi movie for horror fans is The Hidden (1987) (If you liked The Faculty (1998), you’ll love The Hidden). The runner-up would be Ex Machina (2014). Both underappreciated gems in the Sci-Fi genre.
Comedy: I find the best non-horror comedies for horror fans aren’t parodies but surreal comedies that make you feel like you’re in a fever dream. My pick for a non-horror comedy movie for horror fans is UHF (1989) which is one of the three mothers of surreal comedy to me (Pee-Wee’s Big Adventure (1985), Big Top Pee-Wee (1988) and UHF). Runner up would be One Crazy Summer (1986) whose cartoon interludes are worth the price of admission (And is one of the three mothers of John Cusack comedies: Better off Dead (1985), One Crazy Summer and Say Anything (1989)).
Fantasy: Fantasy movies are the lighter side of horror (plays Tales from the Darkside theme…”but not as brightly lit”…). My pick for a non-horror fantasy movie for horror fans is Pan’s Labyrinth (2006). The runner-up would be Legend (1985). Both are fantasy movies whose imagery evokes feelings of horror but are tightly woven into a fantasy setting. (I was going to put in the Dark Crystal (1982) but my inner child is still too traumatized to mention it.)