I think one of the most impacting quotes is from the final chapter when we see Attitcus's advice "in action" so to speak. Scout has walked Boo Radley home, and when she stands on his porch (and metaphorically in his shoes) she can see the street and the events of the past year from his point of view. She relates that she sees in the following:
It was summertime, and two children scampered down the sidewalk toward a man approaching in the distance. The man waved, and the children raced each other to him.
It was still summertime, and the children came closer. A boy trudged down the sidewalk dragging a fishing pole behind him. A man stood waiting with his hands on his hips. Summertime, and his children played in the front yard with their friend, enacting a strange little drama of their own invention.
It was fall, and his children fought on the sidewalk in front of Mrs. Dubose's. The boy helped his sister to her feet, and they made their way home. Fall, and his children trotted to and fro around the corner, the day's woes and triumphs on their faces. They stopped at an oak tree, delighted, puzzled, apprehensive.
Winter, his children shivered at the front gate, silhouetted against a blazing house. Winter, a man walked into the street, dropped his glasses, and shot a dog.
Summer, and he watched his children's heart break. Autumn again, and Boo's children needed him.
This passage completely captures the essence of the novel, and so thoughtfully conveys the theme of looking at the world from someone else's perspective.