I think you should start with fantasy CLASSICS. From what you've wrote you already know Tolkien but have you ever read anything by Robert E. Howard, Lord Dunsany or Clark Ashton Smith? If not, then you SHOULD. If you don't know who these guys are, you don't know what fantasy is.
Here are my recommendations, books that I think are absolutely essential for anyone interested in the fantasy genre:
01. Robert E. Howard - Conan series (classic heroic fantasy, sword and sorcery)
02. Robert E. Howard - King Kull series
03. Robert E. Howard - El Borak series
04. Robert E. Howaed - Bran Mak Morn series
05. Lord Dunsany - anything really, try The Gods of Pegāna or A Dreamer's Tales
06. Clark Ashton Smith - anything
07. Karl E. Wagner - Kane series (heroic fantasy, dark fantasy, horror)
08. Clives S. Lewis - The Chronicles Of Narnia cycle
09. Ursula Le Guin - Earthsea tetralogy (A Wizard Of Earthsea, The Tombs Of Atuan, The Farthest Shore, Tehanu)
10. Ursula Le Guin - The Beginning Place
11. Howard P. Lovecraft - The Dream-Quest Of Unknown Kadath (dark fantasy, horror)
12. Howard P. Lovecraft - The Call Of Cthulhu
13. Andrzej Sapkowski - The Witcher saga
http://en.wikipedia.org/wiki/Robert_E._Howard
http://en.wikipedia.org/wiki/Conan_the_Barbarian
http://en.wikipedia.org/wiki/Lord_Dunsany
http://en.wikipedia.org/wiki/Clark_Ashton_Smith
http://en.wikipedia.org/wiki/Clark_Ashton_Smith_deities
http://en.wikipedia.org/wiki/Karl_Edward_Wagner
http://en.wikipedia.org/wiki/Ursula_K._Le_Guin
http://en.wikipedia.org/wiki/Earthsea
http://en.wikipedia.org/wiki/H._P._Lovecraft
http://en.wikipedia.org/wiki/Andrzej_Sapkowski