I remember reading this book a few months back.
It's about a girl, whose parents were killed by bad guys. She was also injured, I think, but a witch offers her revenge or "life" in exchange for her heart. This gives the witch control over the girl. Later, she's chosen to kill the prince. She meets a guy that helps the people who don't have access to medicine, turns out that guy is the prince. They fall in "love" (well the prince does). The girl tries not to give into the "hunger" (a side effect of her heartless-ness) and when it's time for the prince to die, she prevents herself from harming him. The prince is dumbfounded and now he hates her.
I never got to the second book, but it's a series. I'm pretty sure and the cover is a girl in a cape with a white? (or black) crow at the top.