After a fight where he's forced to remove his mask, Peter uses every ounce of his strength to stop a runaway train. He passes out immediately afterwards, and the passengers catch him and set him down on the floor, whereupon they're shocked to see that Spider-Man is "just a kid." Peter then wakes up and a couple kids give him his mask back, as everyone promises they won't tell anyone who he is. This is capped off by their response to Doc Ock's arrival: one passenger gives him the Go Through Me line, giving another passenger courage to vow the same, and then another, and another, until the entire train car is standing valiantly against him. It doesn't do any good, but the intent was worthy of admiration.
After Spider-Man saves her life, Aunt May realizes she was wrong about him and tells him so.
Aunt May's words of encouragement to Peter:
Aunt May: Too few characters out there, flying around like that, saving old girls like me. And Lord knows, kids like Henry need a hero. Courageous, self-sacrificing people. Setting examples for all of us. Everybody loves a hero. People line up for them, cheer them, scream their names. And years later, they'll tell how they stood in the rain for hours just to get a glimpse of the one who taught them how to hold on a second longer. I believe there's a hero in all of us, that keeps us honest, gives us strength, makes us noble, and finally allows us to die with pride, even though sometimes we have to be steady, and give up the thing we want the most, even our dreams.
Peter's glasses becoming useless again, signifying his powers returning. It happens because he needs to save Mary Jane, proving that he really does love her.
Doc Ock's reaction to learning who Spider-Man is. When Otto first met Peter, he scolded him for what he perceived as laziness in Connors' class. In a movie where Peter's double life sees him constantly disappointing everyone, it's sweet to watch him redeemed, and in the eyes of the film's villain, no less.
Jameson reestablishing his hatred of Spider-Man right after he realizes the hero has returned can put a smile in a fan's face, as weird as it sounds, because it's such a "all's right in the world" moment for Jonah.
The Bugle's triumphant "He's Back!" headline shows Jonah's true feelings: he does want Spider-Man around.note The scriptnotes and novelization explain that part of this is because Spider-Man sells papers and numbers have been down since he disappeared.
Peter rescuing the little girl from a burning building without his powers.
Additionally, the moment in the rescue where the little girl herself tries to help Peter when he's dangling from a hole in the floor. Terrified as she is, it's a brave act for a small child to try to pull him up.
Ursula's random act of kindness in giving Peter some leftover chocolate cake when he needed kindness the most. This scene cemented her Ensemble Dark Horse status.
Peter's first meeting with Otto. While Otto's initially annoyed at having to put up with Harry's friend, he quickly warms up to him when Peter displays his wits. He and his wife also give him relationship advice by telling him about their own romance.
Otto: Did Edison sleep before he turned on the light bulb? Did Marconi sleep before he turned on the radio? Did Beethoven sleep before he wrote the fifth?
Peter: Did Bernoulli sleep before he found the curves of quickest descent?
Otto: (Grinning) Ah Rosie, I love this boy.
Dr. Octavius describing his college romance with Rosie. It's clear that he still adores her after many years of marriage.
Mary Jane's line in the last scene "Here I am, standing in your doorway. I've always been standing in your doorway" has a ton of meta significance when one considers that MJ was first revealed to comic readers around the world... standing in Peter's doorway. Even better? MJ calls Peter "Tiger" shortly afterwards, just as she famously did in her big debut.
Another line from that scene: "Isn't is about time someone saved your life for a change?" Peter has been miserable the whole movie, nothing going right, losing his powers and feeling alone. And here she knows his identity and still wants to be with him and heal his emotional pain. In the end he can only respond, "Thank you, Mary-Jane Watson."
May forgiving Peter for his part in Uncle Ben's death.
May: It's water over the dam, or under the bridge, or wherever you like it. But you made a brave move, in telling me the truth, and I'm proud of you. And I thank you, and I... I love you, Peter. So very, very much.
Robbie standing up to Jameson, even if it falls on the latter's deaf ears. Especially with the implication that Robbie might suspect Peter is Spider-Man.
Jameson: Robbie, here's your page one: 'Masked Menace Terrorizes Town!' Robbie: I told you he's not a menace!
Harry is willing to let Peter be interrogated by Doctor Octopus in order to figure out where Spider-Man is, and has been pissed at him the whole movie for seemingly siding with the man who killed his dad. But what's the thing he yells after the Doctor as he goes off to get him? "Don't hurt Peter!"
Additionally, the way he hesitates when it's time to finally get his revenge. He has the knife, ready to kill the one who murdered his father. But the moment he sees it's Peter he just... stops. No matter his feelings, no matter how he's been waiting to get his revenge, he can't bring himself to kill his best friend.
A small one when Octavius' reactor seems to be working smoothly before the demonstration goes awry: An attendee, presumably an executive of Oscorp, puts a hand on Harry's shoulder to congratulate him on the work he's doing for Norman's company. Harry even thanks him.
Harry arranging for Peter to meet Otto. When Otto says he doesn't have time, Harry subtly reminds him that they're funding his experiment. Harry may be angry that Peter makes money taking pictures of Spider-man, he's still his friend and went out of his way to help him meet an idol of his.
The casual tone Peter addresses Octavius with when he approaches him is heartwarming by itself too. Peter drops all notions of superheroes and supervillains by first addressing the Doctor by his real name and then revealing his true identity to him. This is no longer a superhero battle, it is a debate between two men of science, colleagues, about what needs to be done.
Keen-eyed viewers will notice that Peter actually moves to destroy the reactor himself, only to be stopped by Otto. This is heartwarming on a number of levels - Peter's unflinching courage in the face of a possibly fatal sacrifice, and that he was in no way expecting Octavius to do the deed himself. Revealing his identity to the Doctor was a last resort gamble, sure, but it was still a huge risk, in that he was also implicitly trusting Octavius to keep it secret after the fact. Really, that alone speaks volumes. And then, of course, Otto's decision to die instead, taking responsibility to fix his own mistake and his refusal to let Peter be killed doing it, even though he knows it will mean his own demise.
The video game:
The developers included the Tribute in Light to honor the lives lost during the September 11, 2001 terrorist attack.