Mmm, I see Sandman has been mentioned and rightfully so, but not other single works by Gaiman.

Stardust is a great book with beautiful illustrations (not really a graphic novel). As usual, better than the movie.

Neverwhere is a good book of fantasy below our modern world.

Of course American Gods is a great book of modern fantasy but it has darker overtones and maybe not for everybody.

I'll put in another suggestion of the Discworld series (by Terry Pratchett, if you're unaware). I'd suggest starting anywhere but at the start: in book 1 he was worldbuilding, which IMO generally means he's not at his best. Book 2 is a direct continuation to book 1, so is also not the best to start on. Beyond those, though, any are worth starting on, especially in the middle of his works. I'd recommend Pyramids, Guards, Guards, or Wyrd Sisters as good options to try first. Pyramids has - obviously - an Egyptian theme. Guards, Guards is a story set in the world's wretched-hive-of-scum-and-villainy and centreing around the Night Watch. Wyrd Sisters is a story about three witches, and an orphaned baby prince, and a mad usurping duke...basically it's a parody of Shakespeare's works.

Robin Hobb- Farseer trilogy, Liveship Traders, Tawny Man, Soldier Son Trilogy, Rain Wild Chronicles. I like all her series.

Robert Jordan and Brandon Sanderson-Wheel of Time series

Brandon Sanderson- I like the Mistborn series. I really recommend his new Stormlight Archive series: The Way of Kings and Words of Radiance.

Stephen King-The Dark Tower series

Tad Williams-Shadowmarch series

Elizabeth Haydon- Rhapsody series

Jacqueline Carey- Kushiel Legacy series

Without looking at what other people are writing (edit: and forgetting that I posted here a year ago), here are some of my favorites:

The "Ebenezer" and "Wuntvor" books by Craig Shaw Gardner. Not too in-depth, but a lot of fun. Similar to Asprin's "Myth" series... which leads me to...

The "Myth" books by Robert Asprin. Light-hearted but interesting romps through all sorts of situations.

The "Thieves World" books - various authors.

David Eddings.
Lawrence Watt-Evans.
David Farland.

Joel Rosenberg's "Guardians of the Flame" series.

The early Terry Brooks books (didn't read any after the original Shannara trilogy).

Michael J. Sullivan.
David Daglish.
Joe Abercrombie.
Patrick Rothfuss.
Steven Brust.
L.E. Modesitt, Jr.

Any Warhammer novel.

There's more, but I'll stop here.

Best stuff around seems to be the Belgariad Saga by David Eddings (and maybe his other stuff).

Mainly Tolkien and Jack Vance here.

I tried Robert Jordan (the big books, not the special edition for teenagers). I didn't find them amazing, but still, I enjoyed reading the three first books. After that, it totally goes down hill and I think I quit after book 5...

David Eddings ( although some will say his stories have a very samey feel to them all)

R.A.Salvatore (yes I am a Drizzt fan and I make no apologies for it.a good number of his books make it to top sellers list so som3thing must be good bout them)

Piers Antony ( if you like puns....)

Try Ursula K. Leguin's Earthsea Trilogy...one of the best. Her science fiction is pretty amazing too.

A whole lot different but very good and known since the Japanese movie adaptation is
Diana Wynne Jones's - Howl's Moving Castle
and the following books of this series from Wales.

It's really good and like always way better then the movie of the first book.

Lots of good suggestions here. Good to see someone remembered Zelazny and Brust. Many of the ones already mentioned are authors I'd have suggested as well. I'll just toss in a few more for shits and giggles:

C.J. Cherryh - one of my favorite sci-fi authors, but she's also done a few fantasy novels. The Fortress series (5 books) as well as the Russian stories (Russalka, Yvgenie, and Chernevog) are well worth checking out.

Elizabeth Moon's Deed of Paksenarrion is worth a read as well.

J.V. Jones' The Book of Words trilogy was also quite enjoyable.

Mary Gentle writes some interesting and different fantasy.

And I would also highly recommend Philip Pullman's His Dark Materials trilogy, which I thought were fabulous reads.

I highly recommend Ursula K. LeGuin's Earthsea books. Not a difficult read, but very well-written and something of a breath of fresh air.

I also really like Garth Nix's Old Kingdom series (Sabriel/Lirael/Abhorsen). Especially recommended if you are interested in dark fantasy with a lot of necromancy or in female protagonists.

Also check out Thieves' World, though the subsequent anthologies don't tend to be as good as the first, and Marion Zimmer Bradley's Lythande. It's a fun collaborative dark fantasy series set largely in the corrupt and dangerous city of Sanctuary.

For urban fantasy, my favorite is the Marla Mason series by T.A. Pratt. I believe there's at least one story you can read online for free, although it probably makes more sense if you've read at least the first book.

Going to second the recommendations for Diana Wynne Jones (Chrestomanci + Howl's Moving Castle), as well as for Robin Hobb's work generally.

I loved Riftwar (Raymond E. Feist) as a teen, got into it because of the excellent game Betrayal at Krondor and its mediocre sequel, but on a recent rereading it's not quite as good as I thought at the time.

These here.

I also read a lot of Robert E. Howard, Lovecraft, Clark Ashton Smith, CL Moore from the pulp era.

Karl Edward Wagner's Kane stories, about an evil warrior/sorcerer who is immortal.

Poul Anderson's classic fantasies, The Broken Sword, Three Hearts and Three Lions (where the D&D alignment system and paladin class originated), Operation Chaos.

Charles Saunders's Imaro books are very entertaining. African sword-and-sorcery.

Here is my list of Awesome fantasy novels that I did not see listed, and if one is listed that I missed my apologies :)

BRENT WEEKS: Night angel trilogy

ANTHONY RYAN: Blood Song, a Ravens Shadow Novel book 1

BRANDON SANDERSON: Mist Born trilogy and Stormlight archive (Saw his name, just restating)

HUGH HOWEY: Wool trilogy (Not fantasy, but HIGHLY recommend)

Someone I can't recommend highly enough is <span class="bold">P. C. Hodgell</span>. Extremely good world building and language. Great storyline and well-written likable characters. One of my favourite authors, bar none, and someone I buy in hardback and paperback.

If you really want the huge epics, the Malazan saga by Steven Erikson is excellent. Be warned, each book is HUGE, and you do have to read them as an interconnected story. Hence, epic. You need to invest some time in this series, but after a while (the first 300 pages or so), you'll find you've stayed up all night to read it all.

Guy Gavriel Kay was the guy chosen by the Tolkien family to help edit together Tolkien's notes. Gather from that what you will. Some of his books are rooted in mythology, be it Arthurian (Fionvar Tapestry), medival Italy (Tigana), or Chinese (Under Heaven). Start with Tigana.

David Gemmell is good for the heroic fantasy - cosy armchair reading. Nothing deep, but a good rollicking story.
Same with David Eddings, a more limited plot - group has to travel to find something and stop the end of the world etc. Lots of humour, light epic fantasy if there is such a genre.
Terry Pratchett is more known for the subversion of tropes through humour in my opinion. He takes ordinary situations; rock music, Father Christmas, the Post Office etc. and transplants them into fantasy.
Simon R. Green's Blue Moon and Hawk & Fisher series are again light reading with a more Warren Ellis flavour. That British sense of humour and sarcasm is very present.
You could always go for George R. R. Martin, but be warned, if you are a fast reader, he hasn't finished A Song of Fire and Ice. You'd have to wait for him to do so to know the end! Epic fantasy.
Lois McMaster Bujold is always good. Try The Hallowed Hunt. It's not necessary to read the other two Chalion books first.
David Weber has a particular writing that may not be to your taste. He's most well known for his Space Opera/ Space Navy series, but he has done some heroic fantasy in the form of the Bahzell series. Lots of gods and paladins and really, really evils. ;) He tends to write in terms of black and white. Sometimes, you're in the mood for that, like a good action movie where you can cheer for the good guys and hope/ expect the bad guys to come to some dastardly end.
Mary Gentle tends to stay in the more Middle Ages/ Renaissance type of fantasy, sometimes with a little steampunk thrown in. Ash: The Secret Histories is excellent.

I can't think of any "old"/ classic fantasy writers other than the ones already mentioned apart from Andre Norton.
Also notable mentions are: Robin McKinley, Michelle Sagara (West), Tamora Pierce (children/ YA).