In the U.S., as far as I know,
Sinclair Lewis: I expect he's still taught in some colleges. First U.S. winner of the Nobel Prize for Literature, so he's not entirely forgotten. Our cable channel, TCM, occasionally shows a movie based on one of his novels, so he may not be completely neglected.
Willa Cather: Similar to Lewis as far as current recognition goes, except not a Nobelist. A few of her short stories pop up in anthologies, including
Best American Mysteries of the Century ed. by Tony Hillerman and Otto Penzler. I think a couple of her novels go in and out of popularity.
Eugene O’Neill: His plays are often revived, in particular
The Iceman Cometh and
Long Day's Journey Into Night.
Edna St. Vincent Millay: Occasionally added to poetry collections. No longer as well regarded as once, I think, but probably still taught in survey classes in college.
Robert Frost: His collected poems are still in print in the U.S. A major American poet, at least in the minds of Americans.
Theodore Dreiser:
An American Tragedy is still considered a major American novel.
Sister Carrie maybe a bit less so. The former is the basis of at least one Hollywood movie, and I believe it is still in print, or was when I worked in a bookstore in the early to mid-Oughts.
James Truslow Adams: Didn't know who he was until I saw he'd written a biography of Henry Adams. That rings a distant bell for me.
George Santayana: Major American philosopher when I was a young man, but I don't think he's much studied now.
Stephen Vincent Benet: Major poet in his lifetime, but if remembered at all, I think he's remembered now for some short stories that are at least of peripheral interest to sf/f fans, like "The Devil and Daniel Webster" -- this was included in a collection that came out in 2011,
Demons ed. John Skipp. I read a collection of Benet's stories years ago and enjoyed them.
James Branch Cabell: Seems to be a you-like-him-or-you-hate-him kind of writer. Fantasy readers are probably his major -- if not only -- audience now. Shares the distinction with Lovecraft and Tolkein of being a writer mostly lambasted by the genre boogey-man critic, Edmund Wilson.
Randy M.