1. Divergent by Veronica Roth:
"There is one mirror in my house. It is behind a sliding window in the hallway upstairs. Our faction allows me to stand in front of it on the second day of every third month, the day my mother cuts my hair."
- Even before we learn that Beatrice is from the selfless faction, we get hints of what that faction might be like: one mirror, behind a sliding door (as if hidden for the rest of year? Or perhaps to discourage wantonness?), a very, very specific time for when she is allowed to look at it--and only the time when it is necessary, i.e. cutting her hair. With three sentences, Veronica Roth has already established a strict world/faction that does not seem to tolerate vanity. They are little details, but they're concrete things we can point to about Abnegation. Also, Roth sets a repressive tone that's appropriate for the start of a dystopian novel as filled with violence as hers is... and yet there's also a quiet contemplation - the distance in Beatrice's voice as she lists these facts - that, perhaps, is reflective of the observations Roth will later make on human nature.
2. Fire by Kristin Cashore:
"It did not surprise Fire that the man in the forest shot her. What surprised her was that he shot her by accident."
- On the most simple level, it sets (the mood and tone for the entire book and) the stage for the following scene and catches your attention right off the bat. I also think that this says a lot about Fire. It's more than just her struggles, which you know will be plentiful if men attack her enough that it's become commonplace. It's also that Fire has this sort of conciliatory tone -- instead of bellowing with anger at the way she's been treated, instead of thinking about herself/dwelling on her pain, instead of plotting revenge, her reaction is that of surprise (and of course defense). This establishes a point of comparison for Fire's character development and later self-acceptance.
3. Daughter of Smoke and Bone by Laini Taylor:
“Once upon a time, an angel and a devil fell in love. It did not end well."
- One: the fairy tale quality, which adds enough lightness, I think, to enhance the potency of the tragedy inherent in the second sentence. I particularly love how Laini Taylor managed to introduce the tragedy aspect with such a simple sentence. There's also something about stating that it's a story focusing on "an angel and a devil" that makes it hold more weight, if that makes sense. You know that things are really not that simple, that black and white, especially in a tragedy. Bravo to Laini Taylor for achieving so much with so few words.
I have a lot more than those three, but I didn't want to make this too long of a post ;). What are some of your favorite first lines, and why do you like them?