The movie adaptation of the Golden Compass comes out in December this year. At the movie website, you can find out what your personal daemon would be.
My daemon is Desra, and it coalesced into a raccoon.
The His Dark Materials books are popular with older children and adults, and would be enjoyed, I think, by most Harry Potter fans. The author, Philip Pullman, is an atheist, and the books are fantasy with some science fiction thrown in. There are witches, talking blacksmith polar bears, and discussions of dark matter and quantum entanglement.
The first story, The Golden Compass, was originally published as The Northern Lights. The two sequels, which take you places you'd never thought of in the first book, are titled The Subtle Knife and The Amber Spyglass. There is also another book featuring main character Lyra Belacqua that followed, called Lyra's World.
The daemons are a mystery if you are new to the story. Without too many spoilers, they seem to be people's souls or conscience, on the outside of their bodies in the form of animals. Until puberty, the daemons can change into any animal shape at any time. They can speak out loud, and it is considered to be the most heinous of acts to touch another person's daemon, and act which even causes physical shock. Daemons, though regulary touch and interact with each other.
I love these books, and the movie looks like it will be excellent.