Trying this with reservations.
20th century SF,
1) Flowers for Algernon, Daniel Keyes
2) The Sparrow, Mary Doria Russell
3) A Canticle for Leibowitz, Walter M Miller Jr.
4) Brave New World, Aldous Huxley
5) 2001: A Space Odyssey, Arthur C. Clarke
20th century Fantasy,
1) The Hobbit/The Lord of the Rings, J. R. R. Tolkien
2) Till We Have Faces, C. S. Lewis
3) A Wizard of Earthsea/The Earthsea Quartet, Ursula Le Guin
4) The Dark is Rising Sequence, Susan Cooper
5) The Princess Bride, William Goldman
Numbers 1-4 on both lists show my bias clearly – I admire novels that are good at big questions and complex answers. The numbers 5 are important to me because of their impact in film as well as literature.
I have a lot more reading to do before I can comment on the 21st Century of any genre!
I guess I’ll take a crack at the 20th century stuff—a totally biased POV (what’s been influential on me).
1) Brave New World Aldous Huxley
2) The Left Hand of Darkness Ursula K. LeGuin
3) Dhalgren Samuel R. Delany
4) The Man in the High Castle Philip K. Dick
5) The Martian Chronicles by Ray Bradbury
1) The Hobbit/Lord of the Rings trilogy J. R.R. Tolkien
2) The Man Who Was Thursday G.K. Chesterton
3) Alice’s Adventures in Wonderland and Through the Looking Glass Lewis Carroll [Realized–too late–that this is from the wrong century…]
4) Little, Big John Crowley
5) Land of Laughs Jonathan Carroll
Dark Fantasy Horror (mostly short fiction but in the long form)
1) Quin’s Shanghai Circus Edward Whittemore
1) Falling Angel William Hjortsborg
2) The Magus John Fowles
3) The Wasp Factory Iain Banks
4) The Shining Stephen King
I’ll play, too. No claim to anything here beyond my own personal taste on this particular morning. And with no thought whatsoever of the most “important” or influential works in either genre — a very different list. I’ll leave the 2st cent. to others.
20th Cent. SF:
1. Dune, Frank Herbert
2. Dhalgren, Samuel R. Delany
3. Neuromancer, William Gibson
4. A Scanner Darkly, Philip K. Dick
5. The Fifth Head of Cerberus, Gene Wolfe
20th Cent. Fantasy:
1. Hobbit/LOTR, Tolkien
2. Little, Big, John Crowley
3. Lud in the Mist, Hope Mirlees
4. Mother London, Michael Moorcock
5. The Dying Earth, Jack Vance
What about Reindeer Moon? This is a book I almost never see discussed among sf and fantasy writers but it’s astonishing, kind of sui generis as many such books are.