Twilight: I can do this, I lied to myself feebly. No one was going to bite me - Bella (Not a very memorable quote just a little ironic?) lol
New Moon: I promise that this will be the last time you’ll see me. I won’t come back. I won’t put you through anything like this again. You can go on with your life without any more interference from me. It will be as if I’d never existed. - Edward (Just because it's so sad and shows how much pain it causes him to leave her!)
Eclipse: Bella, I see what you’re doing. You’re trying to make everyone else happy. And I don’t care about anyone else’s feelings. I only need you to be happy. Don’t worry about breaking the news to Alice. I’ll take care of it. I promise she won’t make you feel guilty. - Edward
Breaking Dawn: From that first little touch, the whole world had shifted. Where before there was just one thing I could not live without, now there were two. There was no division – my love was not split between them now; it wasn’t like that. It was more like my heart had grown, swollen up to twice its size in that moment. All that extra space, already filled. The increase was almost dizzying.- Bella!
It's not word for word because I don't have the books in front of me, but it goes something like this:
Twilight: "I don't see how that's any of your business"--stupid shiny volvo owner. "The wasting of finite resources is everybody's business."
New Moon: "I did drown! Crap, crap, crap! This is going to kill Charlie!"
Eclipse: "First, you are bizarrely moral for a vampire."
Breaking Dawn: "Make Bella see sense? What universe do you live in?"
There's tons that I like, but those are the ones that popped into my mind.