The title says it all! I want to know about any good Fantasy series besides the obvious Lord of the Rings and Game of Thrones (although you can still discuss them if you want.)
Suppose you could include historical stories but not romantic stuff ala Downton Abbey :P

I highly recommend Elric of Melniboné/Stormbringer series by Michael Moorcock, The first 5 books in the Wheel of Time series by Robert Jordan, the original Dune novels by Frank Herbert, I Have No Mouth and I Must Scream by Harlan Ellison, The Dark Tower series by Stephen King, or The Incarnations of Immortality series by Piers Anthony.

Pathfinder series by Orson Scott Card. Not his best, but make a pretty good read.

The Farseer Trilogy by Robin Hobb is the best fantasy series I've read.

Raymond E. Feist and his Riftwar Saga.

Weiss & Hickman, I can vouch for pretty much everything not dragonlance. I read 90% of what is already mentionned in this thread, I think 'the death gate cycle' is WAY better (I could add on top of that corum, erekose, Tad Williams things, David Gemmel ..... 'The Death gate cycle' still wins with a pretty large one, IMHO).
All people whom I recommended it loved it. Don't go wiki to learn about this you'll spoil yourself quite easily and that is one of the ten things you still would regret in 50 years.

The Chronicles of Thomas Covenant The Unbeliever by Stephen Donaldson. About 9 books in total.

The Saga of the Exiles by Julian May, dunno how many, 5 or 6 maybe.

I've never moved on since reading Tolkien's main works a LONG time ago : how is it possible for anyone to surpass the king of fantasy ? I own a David Eddings book, Pawn of Prophecy, given to me by a friend some time ago. I keep looking at it but always end up choosing to read something else. I also have a copy of Raymond E.Feist's Magician and that gets the same treatment. I love the amazing artwork on the covers of these books but whenever I start reading one I always find myself comparing it unfavourably with Tolkien's stuff. I suppose I'm a bit stuck in the past. I've heard about Stephen Donaldson's stuff too and love the sound of it.

It might not be describable as fantasy but I own The Necronomicon, a large collection of H.P. Lovecraft's work. I am more likely to read that, or at least some of it, because I own two games : Call of Cthulu : Dark Corners of the Earth, and Fall from Heaven 2, a Civ 4 mod, both of which are based, at least in part in the case of FfH2, on Lovecraft's stuff and reading some Lovecraft might help me to enjoy these games more.

This. So much this. :p

Joe Abercrombie
Terry Pratchett
Lawrence Watt-Evans
Michael J. Sullivan
Dennis L. McKiernan
Raymond E. Feist
David Eddings
Patrick Rothfuss
L.E. Modesitt, Jr.
Glen Cook
Steven Brust
Guy Gavriel Kay
Lloyd Alexander

The Dresden Files and The Codex Alera by Jim Butcher are two of my favorite series.

<3 The Dresden Files! I need to get the new novel soon, sadly that'll have to wait for now. I was even impressed with the series, while it deviated greatly from the books it still kept the heart of the stories. Plus I rather liked the change to Bob that was made from the books; though I really did like both versions of him. I would love to see Paul Blackthorne return to the role in films based along plots of the books. :)

the Black Company and Acacia the war with the mein and ofcourse the wheels of time series

Terry Goodkind's Sword of Truth series is amazing. It mixes fantasy in philosophy into a compelling world.

Brent Week's The Night Angel trilogy is also very good as long as you dont mind a very mature setting (one of its strong points in my opinion)

Terry Brooks is another good fantasy author. The Shanara series is really good though his more recent work with it has been less than satisfactory for me. For the good stuff go back 15-20 years.

Fantasy is a broad area.
Some combination of Sanderson, Butcher, Keyes, Lynch, Williams, Hearne, Brooks, Rothfuss, Brett, Lawrence, Jacka, Cook have a lot to offer depending on your preferences. I could keep going. Eddings and Feist are solid. Abercrombie isn't bad. Weiss & Hickman are okay.