Sure, I'm also a fantasy fan, I'll list off some of my favorites and ones that are on my long 'to read at some point' list. Some are less medieval fantasy than others, but still fantasy nonetheless.
The Wheel of Time series by Robert Jordan, completed by Brandon Sanderson after Jordan's death. One of my all time favorites, probably my second favorite series after A Song of Ice and Fire.
The Mistborn trilogy by Brandon Sanderson. Not quite medieval, but damn is it good. All of Sanderson's other work I've read has been phenomenal too.
The Malazan Book of the Fallen series by Steven Erikson. I've only read the first book of this so far, waiting on the library to get more, but it looks like it'll shape up to be pretty awesome.
The Black Company series by Glen Cook. This is a strange one, not at all the typical fantasy of wizards and dragons, but if you liked Game of Thrones you'll probably be fine with that.
The Shannara series by Terry Brooks. Not the best series ever, but it's got some really cool stuff going on. It's also worth checking out Brooks's other work, such as the Word and Void trilogy (at least I think it's just three) which is a modern fantasy thing.
The Kushiel series by Jacqueline Carey. Uh, this one has a lot of adult stuff happening in it, probably best you avoid it if you're not an adult.
The Discworld series by Terry Pratchett. His stuff is comedic fantasy, not serious stuff, but it's so damn good.
Anything written by Neil Gaiman. Most of his work is modern day fantasy, but it's great, don't pass it up just because of the era it's set in. Good Omens, which he did with Terry Pratchett, is one of my favorite books of all time.
The Sword of Truth series by Terry Goodkind. This used to be my favorite series.. until I read other fantasy series that weren't aimed at kids. I mean, it's not that it's atrocious or anything, just that it has some major issues. Gets really preachy with the author's philosophy, it felt like it sorta dragged on after one of the books, a couple other issues. But then I've also heard some people say it's amazing and defend it against all sorts of criticism, so maybe it's just not my kind of book. If you like the premise, definitely read it.