Good question, and there are quite a few! I'll mention a few of the ones I feel are significant.
I think the first line of the novel is important: "I became what I am today at the age of twelve..." (1). This seems to show that his identity, or the perception of himself, now as an adult was established in his childhood years: he recognizes how his cowardice had a lasting impact in his life.
Hosseini also discusses Baba's perspective on sin: "...there is only one sin, only one. And that is theft. Every other sin is a variation of theft" (17). This is significant because it shows how intuitive Baba is, but it also presents the interesting argument about whether or not Baba is a "sinner" according to his own definition since he never tells Amir the truth about Hassan.
Amir also tells about how he threw pomegranates at Hassan, hoping Hassan would throw them back: "I wished he'd give me the punishment I craved, so maybe I'd finally sleep at night" (92). This shows how much guilt Amir has and how he hopes he can somehow be punished for his cowardice, perhaps alleviating that lingering guilt.
One more important passage was from the "fight" between Assef and Amir (I put it in quotes because Amir never really fought back!). While he is being beaten, Amir quips "...for the first time since the winter of 1975, I felt at peace. I laughed because I saw that, in some hidden nook in a corner of my mind, I'd even been looking forward to this" (289). This might be the turning point in Amir's life where the guilt about Hassan is extinguished, sort of a penance for Amir's wrongdoings.
These are just a few. I've provided a couple e-notes links that might help you if you need more!