May's recommendation: The Last Unicorn, by Peter S. Beagle.

Somehow, I managed to grow up without encountering The Last Unicorn. I'd heard of it, sure, but I never saw the movie until I was twenty-two and in my first year of graduate school. And I never read the book until this month, several years later.
This was, undoubtedly, my loss.
The Last Unicorn is, quite simply, a beautiful book in every way. The language is elegant and unassuming, with occasional bits of unexpected humour; its tone reminds me of nothing so much as a more solid, more solemn sister of The 13 Clocks. It strikes that perfect balance, where you could shelve the book in the adult or young adult or perhaps even children's section of the library, because the language isn't a barrier to the story, but rather the vehicle that takes you there.
The story itself has that odd awareness one can sometimes, if one is very good, pull off in fantasy: the characters have a sense of themselves as characters. Prince Lir determines that he will be a hero to win the affection of Amalthea, a unicorn in the form of a young woman, and then he takes certain actions because those are what a hero in a story does. It's more than the idea of a role model. Lir understands that his life -- that everyone's life -- is a story.
And the story, like all good stories, has both moments of brightness and darkness. It begins with a unicorn living in a wood. She later takes on a human form, but no matter what her shape, she is not a human character. She does not think and feel as humans do. Eventually she hears that unicorns have not been seen in ages -- perhaps have vanished from the world -- and so she leaves her wood, where her presence ensures eternal spring, to go out into the unpredictable, changing, decaying mortal world to search for her kind.
I would not be at all surprised to learn that the writers behind the game Changeling: The Dreaming had read The Last Unicorn at an impressionable age. The world is not a place of unicorns anymore. The people she passes see her as a white mare, because their minds no longer accept the possibility of a unicorn in front of them. And those who see her for what she is are often unscrupulous. There is a twisted circus of mythical animals, some real, others not. There is a town under a curse, whose inhabitants embrace their curse in a twisted fashion, fearing what will happen when the rest of it comes true. There's the manipulative Mommy Fortuna, and the terrifying Red Bull, and Schmendrick, the magician with the sharpest dichotomy between the silliness of his name and the coolness of his nature I've ever encountered in fiction.
If the animated movie looks dated to you and/or the out-of-tune song Amalthea and Lir sing makes your ears bleed, never fear, there's a live-action remake coming, which so far shows every sign of being excellent instead of a travesty. But regardless, you should also read the book, for there's much of beauty in its language, that is different from the visual beauty of a film.
You may want to keep a box of tissues on hand, though, if you're the sort to cry. Because Peter S. Beagle understands that sadness has its place in all great stories.