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.
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.
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.
Peter rescuing the little girl from a burning building without his powers.
Ursula's random act of kindness in giving Peter some leftover chocolate cake. This scene cemented her Ensemble Darkhorse status.
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.