These books are the ones that I'm prepared to call the best of 2013 - that is, that I read in 2013. I offer you no guarantee they were published in 2013, mind.
White Teeth by Zadie Smith: Unlike the other books I've picked, this one isn't remotely new, but this sprawling coming-of-age story reminds me of Edgardo Yunque, whose Lamentable Journey was written around the same time. Alas, Yunque is no longer with us, but thankfully Smith is.
1Q84 by Haruki Murakami: This book, popular enough that you don't need me to introduce it, is fantasy verging on magical realism, quite long, and surprisingly small-scale in its resolution.
2312 by Kim Stanley Robinson: Most of the time I was reading this, I didn't actually enjoy it. What impressed me at the time - and the reason I don't forget it - is the wide range of human habitats Robinson describes. Any one on its own would be lauded as inventive; taken together, its a startling vision.
Cloud Atlas by David Mitchell: The best book I read all year? Likely not. Perhaps it's on here because I was singularly unimpressed with the movie and expected so little of the novel it was based on. The ultimate vision of the novel and the movie are as different as the visions of Do Androids Dream of Electric Sheep? and Blade Runner, and the Russian nesting-doll structure of the book is a far more carefully crafted piece of work than the haphazard chronology of the movie.
Dream of Ding Village by Yan Lianke: A book I likely would have never heard of if I hadn't been faced with a limited English-language selection at the bookstore at Iguatemi Florianopolis, this book tells the story of a Chinese village devastated by the AIDS crisis - with the government's complicity. That the story is told by a ghost makes for a interesting narrative structure without making the novel a part of the fantasy genre.