Over the next few weeks and months you'll probably be hearing a lot about Phlip Pullman's Dark Materials Trilogy. They're the books Harry Potter fans are supposed to "graduate" to � infinitely better prose, richer characters, more complex morality. They're all that, sure, and if nothing else you'll probably want to read the first one before the amazing-looking movie comes out. They are also, unfortunately, a little bit dull after a while. I recognize them as better literature than Harry Potter, but I didn't quite enjoy them as much.
And in any case, they're still children's books. There's nothing wrong with reading children's books, of course, but if you're looking for genuinely brilliant adult literature that shares the Potter spirit, I can enthusiastically recommend Susannah Clarke's epic 2004 novel Jonathan Strange & Mr. Norrell. My favorite aspect of the Harry Potter books has always been the world that Rowling creates, with its fantastic yet credible artifacts, its sense of history and its well-considered rules and regulations. Jonathan Strange is not a fantasy book in the sense usually implied by that term, but it shares the same delight in imagining what a real world (in this case 19th century Britain) would be like if overlayed with magic.
Unlike Potter, Strange is decidedly slow-moving. Its plot is moved forward by the inner lives of its characters, not the onrush of events. But it is, in its own way, utterly spellbinding.
Related: Pimp my daemon.