In 1979, Gary Gygax listed a series of books and authors from which he drew inspiration when designing his Dungeons & Dragons game system(s). These were primarily works of fantasy or science fiction. For an excellent overview of how this appendix influenced tabletop role-playing gaming, I'd refer you to the "Appendix N: Inspirational Reading" section of the Dungeon Crawl Classic RPG rulebook on page 442.
Here, I include my sources of inspiration for fantasy role-playing, some of which will match mister Gygax's list, but much of which has been published since 1979. I am including in this list works of fiction and non-fiction, as some of these non-fictional works have been rather influential in my design of campaigns, adventures, etc. Some of these influences, whether fictional or not, may be slight, and I might have taken a very small thread from a work mentioned and woven from it something much larger or even invisible to my players. For example, why in the world would I have Herman Melville's ponderous Moby Dick herein? Not because I like whales or because I've run extensive maritime adventures (I have not), but because of the sheer maniacal drive of what could be the prototypical overzealous cleric, Captain Ahab, and the enigmatic QueeQueg, who I think would be a marvellous gonzo player character in any adventuring scenario and may or may not appear as a non-player character in anything I might right or run. Other books listed here show a pretty straightforward influence on my judging and playing style. For example, anyone playing in my campaigns who has read M. John Harrison's Viriconium stories will immediately see nods to these works.
Note that I have explicitly NOT included other media. At a later date, I will give my "Appendix M" for other media, such as movies, music, comics, graphic novels, works of art, etc. That may end up being a much longer list than this one!
Note also that some of these are works I have read very recently that I may not have mined just yet, but am working on supplements, adventures, and so forth that will, I promise, dip into these sources. The thing about my Appendix N is that it will always, always be growing!
So without further ado, I give you my list of authors and, sometimes, specific works, that have influenced my gaming: My personal Appendix N.
Dante Alighieri: Inferno
M.A.R. Barker, esp. the Tekumel books, Flamesong in particular
William Barrett: Irrational Man: A Study in Existential Philosophy
Jorge Luis Borges
Ray Bradbury, esp. The Martian Chronicles
Robert Burnham: Burnham's Celestial Handbook
Edgar Rice Burroughs, esp. Mars series
Italo Calvino, esp. Invisible Cities
James W.P. Campbell: The Library: A World History
Robert W. Chambers
Michael Cisco: The Divinity Student
Stephen J. Clark: In Delirium's Circle
Richard Cohen: By the Sword
Norman Cohn: Pursuit of the Millenium: Revolutionary Millenarians and Mystical Anarchists of the Middle Ages
Steven Erikson, Malazan series
Brian Evenson, esp. Dark Property, Fugue State, and The Wavering Knife
Jeffrey Ford, esp. the City Imperishable books
Brian Greene: The Hidden Reality
M. John Harrison, esp. the Viriconium stories and novels
Robert E. Howard, esp. the Conan stories
J.K. Huysmans: Against Nature
Paul Koudounaris: Heavenly Bodies: Cult Treasures and Spectacular Saints from the Catacombs
Fritz Leiber, Fafhrd and Gray Mouser books
Brian May: Diableries: Stereoscopic Adventures in Hell
Herman Melville: Moby Dick
China Mieville: Perdido Street Station
Michael Moorcock, esp. the Elric of Melnibone books
Edgar Allen Poe
Mark Samuels, esp. The White Hands and Other Weird Tales
Clark Ashton Smith, esp. the Zothique stories
Arkady Strugatsky: Roadside Picnic
Jack Vance, esp. The Dying Earth
Jeff VanderMeer: City of Saints and Madmen
Gene Wolfe, esp. Book of the Long Sun and Book of the Short Sun novels