Code Lyoko has a few of these, including Sissi's kiss in "Ultimatum" and the near-death in "Cold War", but the standout example is the final part of the Season 2 ending, "The Key". The final two episodes of the season are an emotional rollercoster for Aelita, eventually leading to the return of her memories and the realization that she is not an AI, but a human being. At the end, though, these lines define the moment:
Aelita: The fight must go on. After all, fighting XANA is my job. Jérémie:(motions for everyone to join hands) No, Aelita. It's our job.
The first-season episode "Frontier", in which Jérémie becomes trapped in the limbo between Lyoko and the real world. The part at the very end: For but a single, brief second, Aelita and Jérémie's fingers touch across the void, before Jérémie is yanked back to the real world. It's not just that they want to be together. They deserve it.
Aelita and Jérémie are pretty good for this trope generally. this troper's favorite moment comes from "Double Take". After discovering that her new costume comes with angel wings, Aelita briefly stops to comment "Jérémie, you are the wind beneath my wings" before swooping down to save Yumi. Cue Jérémie blushing.
There's also the scene in "Zero Gravity Zone" after the Return to the Past where Ulrich looks into the audience to see his parents sitting there just like before the whole gravity-reversal mess started...then he glanced over a little bit further to see his three friends sitting on the side-lines. One almost gets the feeling that it means just as much to him that his friends are there this time that his parents are (considering what kind of a guy his father can be at times, one can easily see why.)
Also in "Zero Gravity Zone", even though he's an emotionally abusive Jerkass, when Ulrich's father is about to be lifted into space and Ulrich is trying to save him, he actually says "Goodbye, Ulrich....I'm proud of you! Really, I am." before letting go so that Ulrich doesn't get dragged up with him. He may not be the best father in the world, but he does love his son deep down.
The final episode, "Echoes", was full of these.
When William is finally free of Xana's control.Ulrich and Yumi are in the scanner room when William (who's finally back to normal) emerges from the scanners. Their first reaction is to hug him.
An earlier example is when Milly, Tamiya, Ulrich, and Sissi are trapped in the cafeteria in "Claustrophobia." As Milly is crying from her fears of not being able to get out of the cafeteria, with Tamiya comforting her, Sissi bends to their level (phone up to her ear), and tells them that "The firemen are on their way," in a gentle, whispered tone. Sissi helps her classmates the best she could in that episode. Another case of Big Sister Instinct.
At several points in the series, particularly in season 4, moments where Hiroki isn't being an Annoying Younger Sibling with Yumi can be very touching.