Wouldn't it depend on who you're offering suggestions to?
For s.f. fans, again depending on their reading habits, I'd suggest The Island of Dr. Moreau or Invasion of the Body Snatchers or I am Legend or a variety of short stories like "Who Goes There?" or "Sandkings." (I'm certain there are more recent examples of s.f./horror but none are coming to mind besides Blindsight which I haven't read.)
For fantasy fans, I might suggest Our Lady of Darkness or The House on the Borderland or The Land of Laughs or The Fisherman. For some fantasy fans, The Only Good Indian might also be of interest given the source of its mythology.
For readers of literary fiction I'd point at The Haunting of Hill House, Beloved, Lovecraft Country, Perfume, Ghost Story, The Red Tree and/or The Drowning Girl, A Headful of Ghosts as well as The Land of Laughs. If the reader is open to short fiction the potential reading list really opens up and includes writers from J. Sheridan Le Fanu and Poe to Walter de la Mare and L. P. Hartley to Peter Straub and Lisa Tuttle and Thomas Ligotti and Caitlin R. Kiernan, among others.
For readers of cozy mysteries, there are a lot of older ghost stories they might already have come across -- I could see them getting into M. R. James, E. F. Benson, E. Nesbit, L. P. Hartley and Agatha Christie since there's a good sized collection of her supernatural/horror/ghost stories out in the world. Meanwhile, for readers of noir mysteries, there are a lot of potential suggestions, from Night Has a Thousand Eyes to Perfume (arguably it's Gothic, but then noir shares a lot of of it's DNA with Gothic) to Something More than Night.
Readers of thrillers are already part way to reading horror if you check out selections like Red Dragon, The Silence of the Lambs, Final Girls and A Headful of Ghosts among a lot of others. And if they've already read Michael Koryta's non-supernatural thrillers, he's written three with supernatural overtones.
For readers who want an adventure, I'd suggest Fury from the Tomb (seriously, I would) and Something More than Night and The Ridge and The Cypress House.
And, frankly, there are flavors of King for most tastes, from Salem's Lot to It to Pet Semetary and well beyond.