I know there are less than a dozen of us who think so, but I'm siding with Conan. Why, you ask?
Well here's the thing. The mythology of Robert E. Howard predates everything else on the list, and is largely responsible for any and all nerdery to this day. Just as we can draw a line from Dungeons and Dragons to the rest of modern gaming, we can draw a line from Conan, Kull, Bran Mak Morn and Solomon Kane to modern fantasy. And...back to Dungeons and Dragons. That's right kids! I posit here and now that without the varied, interesting, explicit and gorgeous fiction of the 15 original stories of Conan, WE WOULDN'T EVEN GAME THE SAME WAY.
Star Wars drew from "Hero With 1,000 Faces" to find archetypal crusaders, villains, rogues, and what--for lack of a better term--we'll call NPC's. Conan has been every one of these, and liaised with even more of them. Star Trek took the possibilities of the Star Wars universe and tried, quite successfully I might add (although I prefer Star Wars and grit my teeth whenever I have to extol anything Trekish) to realize the sort of world where the damn-near-mythological technology and prowess present in Star Wars in a world bound by Newtonian mechanics. Batman's consideration of ethics has been greater than that of most religious groups over the course of his run, but it was that consideration that moved or stayed Conan's hand over and over again from the time of his youth to his appointment to king of Aquilonia. You can see the gears turning in his head as he considers the right and wrong of his actions, despite their relative ease and his lack of consequence at most times.
I don't consider the rest of the works here as qualifying opponents to Howard's work. Star Wars, Star Trek and Batman took components of nerdery and followed them to their logical conclusions. Thank God. They are each beautiful and essential to our culture in their own ways. The world is more beautiful and interesting because they exist. Still, they each owe s debt to everyone's favorite Cimmerian. Without him, they might not be.
Also, inb4 "lol Ahnold hur hur hur." Try to disregard the two hours of the Governator (that I actually dig, thank you) and read a fucking book. These stories predate more of our grandparents. And yes, that's older than Lord of the Rings.