Robert E. Howard- and he wrote a lot of other stuff besides fantasy.
Tolkien of course
anything in the old Ballantine Adult Fantasy series, some great classics from William Morris, Lord Dunsany, E.R. Eddison, James Branch Cabell,etc
as you see, I favor older authors.
Still, there is some more recent good material too- have been reading some Anne Bishop.
Depends on how narrowly you define fantasy- is Edgar Rice Burroughs fantasy or adventure? Or H. Rider Haggard? Two of my favorites. If the "lost race" subgenre is considered fantasy, certainly yes, and of course A. Merritt.
Find the YA Section of libraries and bookstores worth checking out. Finally got around to the Narnia Chronicles and glad I did. And John Flanagan.
Seems that so many more modern favorites are mine are women writers. Besides Bishop, really like Mercedes Lackey and Sara Douglass.
And of course Marion Zimmer Bradley. Darkover is as much fantasy as sf, and of course her wonderful Sword and Sorceress anthologies.
Like the Celtic/ Arthurian genre whether or not it has a fantasy element like Bradley or Evangeline Walton, or more strictly historical fiction like Rosemary Sutcliff or Jack Whyte.