Some recommendations from more years of reading fantasy than I care to admit to.
Firstly a warning - be careful of series that are not yet finished. I started reading the Wheel of Time series in 1991. The last book is still to be released 21 years later (expected Jan 2013), written by a different author because Robert Jordan passed away.
A Song of Ice and Fire is really good - but not finished yet and epic fantasy takes time to write well.
Some of these have already been mentioned so take those as my endorsement
If you want an easy entry into Fantasy as a step up from Potter
David Eddings - Belgariad. Really easy to read, engaging characters and standard fare. Only need to read one of his series' as they are all the same with different names
Anne Mcaffery - Dragonriders of Pern. Great reads, starts out fantasy but turns sci fi as it goes through books. She also did a great pure SciFi series, the ship who sang.
Brandon Sanderson - pretty much anything. The mistborn series is a good start. He is really prolific writer too so lots to read.
Getting into the more standard fantasy fare - good to go to once you have read LotR
Tad Williams - Memory, Sorrow and Thorn. The classic orphans discovery of his true power tale with a bit more meat on it than Eddings. Williams has a great cyberpunk/scifi series called Otherland as well
Raymond Feist - Magician (et al.). I have read the original trilogy multiple times, and it is still one of my favorites.
Terry Brooks - a little up and down I have found, but the Shanara series is solid.
Terry Goodkind - Sword of Truth. Goes some weird places in later books but is an enthralling read.
Robin Hobb - Buy everything she has ever written now! Start with the Farseer trilogy or The Liveship Traders and then continue. A truly engaging and brilliant writer than has produced some of the most memorable and moving characters and stories ever invented. If you like your heroes to have real flaws and to experience the tragedy of the story rather than observe it go here.
Robert Jordan/Brandon Sanderson - Wheel of Time. If you can get through the already written 12,000+ pages before the last book comes out I will be impressed. This story is more of an experience than a book.
Getting a bit out there - of you want something a bit out of the ordinary
Stephen R Donaldson - The Ballad of Thomas Covenant. A story of alternate world travel and power differentials, and belief. You will want to punch Thomas in the face at times.
Roger Zelany - Chronicles of Amber. Another alternate realities version of a fantasy world, but with a bit more acton in a more sprawling universe than Donaldson. Less annoying protaginists too
Mervyn Peake - The Gormenghast trilogy. This book is really hard to get into as the world is very different and not explained at the start. The language is mesmerising though and it will draw you in and transport you. The closest I have seen this genre get to literature. This is an old series, predates LotR, but after the Hobbit, and is one of the creators of the Fantasy genre.
Hope this helps