A Song of Ice and Fire - The first book has been made into the first season of the HBO series Game of Thrones, so this series has become rather popular. This novel is the ideal of the type of 'good' fantasy I'm trying to advocate. It has everything - complex character, plot, very well-written, etc. It's my favorite fantasy series. (Tip: If anyone's read this series and liked it and wants more like it, try reading Acacia, not nearly as amazing but very similar and still really good, like asoiaf on a smaller scale with 9/10 instead of 10/10 elements).
The Gentleman Bastard Sequence - The first book is called The Lies of Locke Lamora. This is a fantasy that feels a lot like non-fiction literature. Even most of the cliches are gone from this series. It's mostly a heist story. It did not interest me at first, and I found it a bit boring until about half way through the first book. By the end of the second book though, it was one of the most entertaining series I'd ever read. It was clever, funny, and sad at times. The characters have depth that is shown through actions and words more than thoughts. It expresses surprising gender equality. It's hard to explain what makes this series so great without actually reading it.
The Farseer Trilogy - This is the most real-feeling fantasy series I've read in my life. The author has no empathy for what happens to her characters. I think this is even more real and raw than ASOIAF. Written in first-person, this doesn't even feel like a story being written. It feels like a real experience being told. You go through an entire book expecting that someting will happen, then it doesn't. As in real life, there is no force shaping the world and guaranteeing a certain outcome.