Great Tales of Terror and the Supernatural ed. Herbert Wise & Phyllis Cerf
The Dark Descent ed. David Hartwell
After those essential anthologies covering the whole of ghost/horror fiction get a bit sparse on the ground. There are other significant anthologies, like theones mentioned here earlier, Frights and Dark Forces by Kirby McCauley.
Recently Otto Penzler, a noted mystery anthologist, has been pulling together horror anthologies: The Vampire Archives and Zombies! Zombies! Zombies!; from what I've read of the stories included, those are must-haves for those monsters. (The Vampire Archives looks to me to have supplanted Alan Ryan's anthology, Vampires -- it was reissued under other titles, as well -- as the standard volume.)
Ghosts are usually popular, and The Oxford Book of English Ghost Stories, The Oxford Book of 20th Century Ghost Stories, both edited by Michael Cox and R. A. Gilbert, are fine anthologies. I haven't read them cover to cover, yet; they're books I enjoy dipping into, which also describes two recent collections of Lovecraftian materials that seem important: The Book of Cthulhu edited by Ross Lockhart and New Cthulhu: The Recent Weird edited by Paula Guran.
I find it easier to come up with a list of essential single-author collections: Start with any sizable, representative collection of the stories of E.T.A. Hoffman, Poe, Nathaniel Hawthorne, Ambrose Bierce, H. G. Wells (a good deal of his s.f. could easily be argued to be horror; Great Tales ... includes two stories by him), Saki, M. R. James, Walter de la Mare, Lovecraft, and Richard Matheson. (I don't mean to suggesst this is a complete list.)
Individual titles I'd suggest,
Ghost Stories of Edith Wharton
Hauntings by Vernon Lee
The Collected Ghost Stories of E.F. Benson
Supernatural Tales by Henry James
Kwaidan & Six Chinese Ghost Stories by Lafcadio Hearn
The Three Imposters & Tales of Horror and the Supernaturalby Arthur Machen
The Best of Algernon Blackwood
Fancies and Goodnights by John Collier
Northwest Smith by C. L. Moore
Zothique by Clark Ashton Smith
The Travelling Grave by L. P. Hartley
The October Country by Ray Bradbury
Twelve Tales of Suspense and the Supernatural by Davis Grubb
The Bloody Chamber and Other Stories by Angela Carter
Nightmares and Damnations by Gerald Kersh
Alone With the Horrors by Ramsey Campbell
Wormwood by Poppy Z. Brite
The Feesters in the Lake by Bob Leman
Extremities by Kathe Koja
The Two Sams by Glen Hirshberg
The Early Fears by Robert Bloch
Night's Black Agents & You're All Alone by Fritz Leiber
Revelations in Black by Carl Jacobi
Collections I haven't read or haven't finished or that only include a few (but significant) horror stories that strike me as probably essential:
The Howling Man by Charles Beaumont
Who Fears the Devil? by Manly Wade Wellman
The Fantasies of Robert Heinlein
In a Lonely Place by Karl Edward Wagner
Randy M.