The books I'm going to list are immensely supermegafoxyawesomehot and I totally recommend them to EVERY SINGLE PERSON WHO IS ALIVE. They haven't necessarily been published in 2013, but they're my favorite ones that I read for that year.
I can't be bothered to give you a reason as to why I loved each of these books as much as I do, but just trust me when I say that they're 100% worth it.
5) Divergent by Veronica Roth
4) Angelfall by Susan Ee
3) Sweet Peril by Wendy Higgins
2) Obsidian by Jennifer L. Armentrout