In terms of sheer influence alone, it is almost irrefutable and undeniable that the genre defining J.R.R. Tolkien would be the greatest modern fantasy authour. The vast majority of medieval fantasy literature that followed The Lord of The Rings, and also role-playing games by virtue of Dungeons and Dragons, very much follows in the footsteps of that work. I would even go so far as to state that a great many of the medieval fantasy worlds, especially the campaign settings devised by TSR, are rather derivative of Middle Earth.
For similar reasons, other highly influential, genre shaping fantasy writers of Tolkien's time that also deserve honourable mentions include The Lion, The Witch and The Wardrobe authour C.S. Lewis and Conan The Barbarian authour Robert E. Howard. Although H.P. Lovecraft was of course a horror authour, I also feel that he likewise deserves a mention here for his contributions.
As for more recent fantasy authours, I must salute George R.R. Martin and his highly popular A Song of Ice and Fire series for its grand scope and more realistic, low magick, high intrigue, and very adult take on medieval fantasy! I also feel like Neil Gaiman deserves high praise for his numerous urban fantasy writings, especially his The Sandman series, Neverwhere, and American Gods. Ditto for Alan Moore and his work on Saga of The Swamp Thing and Watchmen. Although I've personally never read any books written by J.K Rowling or Terry Pratchett (with the sole exception of Good Omens), I cannot deny their own influence and popularity.
