I recomend Robert Jordan’s, “The Wheel Of Time”, George Martin’s “A Song Of Fire And Ice”, and Terry Goodkind’s “The Sword Of Truth”.
I would also recomend John Marco’s first series, which is three books in length. I forget what it’s called, but the first book is “The Jackel Of Nar”, and second,“The Grand Design”. It’s a great series, plus you don’t have to wait 2-3 years for his releases, like you do with Jordan and Martin.
I’ll ‘third’ the mention of George R.R. Martin’s “Song of Fire and Ice” Series. Great, gritty, realistic, but still escapist.
I’ll second the Charles de Lint nomination too. Hornswoggler seems to have my taste in books, as his list closely mirrors my own preferences. I was going to mention de Lint along with Tim Powers, whose stories are maybe more ‘fun’. de Lint excels in having strong female characters.
Can’t believe I forgot Steven Brust. Phoenix Guards and Five Hundred Years After are great stories in the Dumas style with lots of subtle humor in the dialogue. The Vlad Taltos books are also good.
Don’t overlook the ‘Harry Potter’ books or the Philip Pullman books (Golden Compass, and sequels) because of the Young Adult tag. Fun reading, good stories, and in the case of Pullman more adult than you’d think.
I’ll have to check out the Morrow books myself.
Actually, that’s six books, or two trilogies. The first book is Lord Foul’s Bane. Damned good fantasy.
Lord Dunsany:
The King of Elfland’s Daughter
Lilith
Hannes Bok:
The Secret of the Golden Stair
Lud in the Mist
William Morris:
The Well at the World’s End
H. Rider Haggard:
She
King Solomons Mines
Alan Quatermain
The People of the Mist
Edmond Hamilton:
Planets in Peril
Clark Ashton Smith:
The City of the Singing Flame
Xiccarph
William Hope Hodgeson:
The House on the Borderland
The Boats of the Glen Carig
The Nightland
These are some of the immortals who helped found the entire genre of adult fantasy. I really recommend Clark Ashton Smith for his vivid landscapes and macabre tinge. Hodgeson is also one of the great geniuses of fantasy writing. If you read all of the books listed here you will have an instant appreciation for nearly all that has come after these giants.
Well, keeping in mind a preference for series, here are some of my suggestiongs:
-Katherine Kurtz’s Gwynedd/Deryni novels. I believe it’s currently four trilogies, with a new book just out that I don’t know whether it’s the start of another trilogy or not. I like the Camber trilogy best (Camber of Culdi, Saint Camber and Camber the Heretic), but you might need to read the Deryni Chronicles trilogy (Deryni Rising, Deryni Checkmate and High Deryni) first, to get a grounding in the world. (Strangely enough, I’m saying that even though the Camber books occur about 200 years earlier, chronologically. Deryni Rising was the first written and I think it works out better to read the earlier-written trilogy first.)
-This is SF rather than fantasy, but I have to plug the Liaden Universe novels, by Sharon Lee and Steve Miller again.
-L.E. Modesitt’s Recluce novels. They’re all over the place, chronologically, but I strongly recommend reading them in the order they were written rather than the order they take place.
-Michelle West’s Empire/Dominion novels (these have been out long enough that they should have a collective name, but they don’t). I like Hunter’s Oath and Hunter’s Death better than the later Sun Sword trilogy.
-The Silver Wolf, Night of the Wolf and The Wolf King by Alice Borchardt. The Silver Wolf must be read first. Don’t even read the back cover summaries of the other two before reading The Silver Wolf, as they give away a surprise.
-And a stand-alone book, Talion: Revenant. I don’t recall who wrote it and I can’t find my copy. I think one of my sisters swiped it.
I’ll also add my vote to Brust’s Taltos novels. I haven’t read Phoenix Guards and Five Hundred Years After yet.
Harry Potter 
I’m twenty-six years old, and I gotta admit, that series KICKS ASS! Read it twice.
Me too’s on (most) of the ones above, plus…
Glen Cook: the Black Company series (rather dark, but good) and the Garrett, PI, series (picture the stereotypical gumshoe in a fantasy world…the earlier books are better)
Wizard’s First Rule, by Terry Goodkind (first book of the Sword of Truth series) is my favorite. It’s like, 900-some pages long, and there’s now 6 books in the series (or 5, I can’t remember off the top of my head). I’ve run into people scoffing at it for reasons I’m not sure of, but I loved every page of it and was hooked in the first two chapters. Great series…full of “cool”. 
- Tsugumo
While agreeing with several of the earlier mentions (Start Feist’s work with Magician, it is both his first work and the first chronologically, everything else (except Faerie Tale) follows from it. He wrote the related trilogy with Janny Wurts, the first book in it is Daughter of the Empire, the trilogy is excellent.) I also want to mention Katharine Kerr’s Deverry books. The first is titled Daggerspell and she is up to I think 12 books. There should only be one or two more in the cycle. The worldview and culture is celtic, and the plot and storytelling is twisted like a celtic knot. It is wonderful reading.
Harry Turtledove’s Videssos books are excellent. The Misplaced Legion is the first of four, and he has written several other series based in the same world. All of them very good.
Lawrence Watt-Evans has written a lot of Fantasy. His Ethshar books are a lot of fun. They are each self-contained but set on the same world. There are some crossover of characters, but you don’t have to have read them in any order. He has also written Touched By The Gods, a stand alone, and Dragon Society the first in a trilogy with the second out sometime soon.
Kate Elliot writes both SF and Fantasy, right now she is finishing up a 5 book series called Crown of Stars set in a middle Europe analogue where magic works. The first book is titled King’s Dragon. Big fat fantasies that are great reading.
I’d concur with many of Zenster’s recommendations, but would like to point out a) that Lilith is by George MacDonald, not Lord Dunsany (I’d guess this is a forgot-to-type-the-author-line sort of deal), and b) although the rest of William Hope Hodgson’s output is certainly worthy of consideration, I have in my hand a piece of paper (well, all right, I have on my hard disk a text file) exploring in some detail the reasons why The Night Land stinks like a week-old elephant seal carcase trapped in a sewer outlet on a hot summer’s day.
Oh goody fantasy novels. You should really try the Amber novels by Roger Zelazny. Anything by Terry Brooks. Orson Scott Card The Tales of Alvin Maker. Terry Goodkind Sword of truth novels.
I can’t believe no one has mentioned C. S. Friedman’s Coldfire Trilogy
Also:
Jack Vance - Lyonesse Trilogy is very good (actually I like pretty much everything he writes)
Second that.
The Author is Stephen R. Donaldson, and the first trilogy is The Chronicles of Thomas Covenant the Unbeliever. The books are Lord Foul’s Bane, The Illearth War, and The Power That Preserves.
Then you have the second trilogy - The Second Chronicles of Thomas Covenant: The Wounded Land, The One Tree, and White Gold Wielder.
You should read all six and just wallow in it for a couple of months. Once I started, I couldn’t get my head out of it. Great stuff.
As a warm-down from all that, Mordant’s Need is good.
I’d second Roger Zelazny, his Amber books. They’re available in one big, thick paperback now. Tremendously fun stuff, and personal favorites.
Also Lord of Light, by Zelazny.
The Stars My Destination by Alfred Bester. Also fun.
The Man in The High Castle, Philip k. Dick. Not nearly as fun, but thought-provoking, anyway.
You can’t go wrong with Zelazny, though. He’s one of Neal Gaiman’s biggest influences, and Gaiman’s damn good in his own right. American Gods, which somebody mentioned above, was excellent, although it really fell apart in the 2nd half. It felt like it needed to be four or five books.
I too enjoy Zelazny’s Amber books.
Two other fantasy books I have read and reread are Elizabeth Moon’s The Deed of Paksenarrion and The Legacy of Gird.
These are books of medieval culture and fantasy, but also the author’s worldbuilding describes both peasant and military life in gritty detail.
Have you read any of the fantasy that Larry Niven wrote? Interesting stuff…two novels that I know of, The Magic Goes Away and The Burning City. He also wrote a lot of fantasy short stories.
I don’t care for fantasy much myself, but I really enjoyed Chris Bunch’s ‘The Seer King’. It has an amazing setting, it combines elements of ancient Roman, Celtic, and Hindu cultures and mythologies. When I first read it I thought maybe it was supposed to be in an alternate history where Rome conquered India, but it’s apparently just a fantasy setting which borrows elements from reality. Anyway, it’s quite dark and gritty, the story moves along quite quickly, and it pays a lot of attention to military tactics…good stuff.