The look on the convicts' faces as they hear the beautiful strains from Le Nozze di Figaro play over the loudspeaker. This is probably the first time any of them have heard music in quite a long time, and the overhead shot of them staring at the loudspeaker in unbridled awe doubles as quite an effective Tear Jerker.
Tommy's Undying Loyalty towards Andy. When Norton question him on Andy's innocence, Tommy repeatedly states that he would be willing to stand before a judge and swear on the Bible if it meant Andy could walk out of court a free man. Norton murders him in response, as he figures he cannot allow Andy to walk free - ever.
All of Andy's attempts to help the prisoners make something out of their lives in prison with his library, and his helping them prepare for after they get out. Given the heartbreaking fate of Brooks this becomes all the more poignant.
Not to mention the library's name: Brooks Hatlen Memorial Library. The prisoners won't soon forget exactly why they're preparing for life on the outside.
The scene at the end when Red finds the package Andy left for him. After a whole movie of having believed that hope was "a dangerous thing", Andy has proven him wrong and has now given him something to hope for as well. The real CMOH of this scene, however, is sealed with the closing portion of the letter:
Andy:Remember Red, hope is a good thing, maybe the best of things, and no good thing ever dies. I will be hoping that this letter finds you, and finds you well. Your friend, Andy.
Quite simply the ending: Red meets Andy on that Mexican beach, both of them free as a bird and as happy as can be to see each other again. The smiles they exchange and the way they run up to each other and hug says it all, by holding on to hope that they would be free one day, their spirits finally triumphed over all obstacles.
Red: I find I'm so excited, I can barely sit still or hold a thought in my head. I think it's the excitement only a free man can feel, a free man at the start of a long journey whose conclusion is uncertain. I hope I can make it across the border. I hope to see my friend and shake his hand. I hope the Pacific is as blue as it has been in my dreams. I hope.
And the Pacific is blue in that beautiful final shot.
A small one while Andy is in extended solitary, where even the guards aren't supposed to talk to the prisoners, one of them whispers this through the food slot to help Keep Andy going:
Guard: "The kid passed. C+ average. Thought you'd like to know."
After returning from his solitary confinement stay due to the loudspeaker incident, Andy is playfully teased by Heywood, who says he would have preferred if he played "something good", like Hank Williams, to which he apologizes by saying they stopped him before he could take requests. Then, many years later, after having substantially improved the library, Andy finally manages to fulfill Heywood's request by amassing a substantial collection of Hank Williams' records.
A small one at the Red's parole hearing in 1967. The previous parole board had treated him with contempt. This time, he is asked to sit down. And parole board lets him go after he sincerely explains the problems he has caused himself.
One for Heywood early in the film. When the new inmates have their first night at Shawshank, he quietly begs the fat inmate to stop crying, knowing full well that Hadley will beat him for it. He's noticeably upset the next morning upon finding the man died of his injuries.
It's easy to forget when rewatching, but the scenes of Andy's last night in prison, and the realization that he didn't come out for roll call the next morning, are all put together to make it look like Andy has been Driven to Suicide. Seeing the Once More, with Clarity! version of events for the first time is simply uplifting.
It's a small moment, but a big one: After Red's second parole hearing, Andy gives him a new harmonica, even apologizing for having to go through one of Red's contraband competitors so that it would be a surprise. Red is genuinely touched by this act of kindness, but doesn't play it. However, later that night, after returning to his cell, Red takes out the harmonica and blows a single, soft note.
Even more heartwarming when you consider that Red had only mentioned playing harmonica once before, in the exact same conversation where Red said that hope was dangerous. In playing the harmonica, even for one note, Red shows that not all hope is extinguished for him.