In "X.A.N.A. Awakens", despite Ulrich being much more cold towards, well, pretty much everyone, he still personally takes Jeremie to the nurse after Jeremie gets zapped by one of the vending machines and after his spar with Yumi, refers to Jeremie and Odd as his friends despite not having known them (personally in Jeremie's case) very long.
After the first Return to the Past erases Jeremie's memory, the other three are upset that he doesn't remember their budding friendship and when Aelita tries to convince the others to give up on her, they're perfectly okay with giving up normal lives to help her.
In "Cold War," snow is on the ground, and people are pelting each other with snowballs. Ulrich even chases Yumi with one he just made himself, and Odd is not too far behind them with a bigger wad of snow. In that moment alone, it's heartwarming to know that even though they are Lyoko Warriors, practically tense for any danger that may come from their Big Bad, they are still just kids.
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 roller coaster 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.
And as he comes out of the scanner, Odd, Ulrich, and Yumi not only carry him to his room and lay him on the bed, they all watch over him until he wakes up. And when he does, the viewer can feel the relief around the three. They take the time to ask how he feels, and when he tells them, the cheering makes it all stronger.
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.
In "Marabounta", as the titular monster eats away at Lyoko and threatens to kill Aelita, XANA does the unthinkable: He sends in monsters to protect Aelita and the Lyoko Warriors. You might argue that he simply doing it because he couldn't let Aelita die without retrieving her memories first, but then once the Marabounta is destroyed, guess what he does? He has his monsters stand back and allow the Lyoko Warriors to leave in peace. Never has the Even Evil Has Standards trope been more heartwarming.
After the Marabounta is gone, before leaving, XANA's monsters even bow to Aelita before leaving. Jeremy may have been right about XANA still being the enemy, but he can't deny that what they had that episode was a truce, no matter how brief.
This line from Aelita upon realizing what XANA is doing. The adorable tone of her voice only enhances it:
Aelita: They're....protecting me!
In "Opening Act", Jeremie is upset that Aelita is spending time away from him to pursue a potential musical career. When her mix track wins a contest to join Jim's rock star nephew to make a music video, she is away on a mission and unable to come forward to claim this prize. When Jim's nephew asks Jeremie if he knows who Aelita is at the end of the ordeal, Jeremie doesn't reply and sets a Return to the Past, looking like he's sabotaging Aelita. Cue the ending, where Jim's nephew comes to Jeremie's room, tells her that her track has won, and leads her off for her prize. When Aelita asks how he knew where to find her, he says a friend of hers sent him a message. And cut to Jeremie, smiling in happiness for Aelita. It shows that even with his negative feelings on the matter, Jeremie would never do anything to stop Aelita from chasing her own dream.
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. Most notably:
Jeremie comforting Aelita as she reminisces about all the emotional pain she's had to go through over the course of the series, and Aelita expressing relief that at least it's finally over and she can move on to a life that's more simple and happy.
Ulrich and Yumi having another almost-kiss, although it is cut short by a Return to the Past AGAIN.
Sissi being invited into the group. Ulrich says it not as though he's offering friendship but as though Sissi already IS and has been their friend which, despite constant memory wipes, is more or less true. Sissi's disbelief turned joy at her secret dream being realized and the fact that it's Ulrich who makes the invitation after having been the one to cause the feud between the group and Sissi to begin with back when he was more of a jerk just makes the moment even sweeter.
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.
In that same episode, Herb becomes hysterical and tries to escape the cafeteria, risking his life doing so. The other students stop him and talk him down, with Sissi coming over to soothe him and actually offering her hand for him to hold.
Another Sissi moment comes at the start of "Deja Vu." Aelita has had another waking nightmare and has gone to the bathroom. Sissi comes in and yells at her for waking her up...and then Aelita just starts crying, overwhelmed with stress and emotion from these nightmares. Immediately, Sissi's demeanor changes (the actual episode script even describes it as "all traces of anger vanish from Sissi's face"), and when Jim comes in, Sissi tells him "It's Aelita Stones, she's not feeling well!" in a concerned voice. She and Jim then help support Aelita back to her room. It further shows that no matter how bitchy she acts to people, when they are in genuine emotional distress Sissi's kind and nurturing side comes out to help them.
The end of "Kadic Bombshell". Putting the Ship Tease nature of it aside, Odd's remark on "That's the Sissi we all love!" is enlightening. The group's relationship with Sissi for the whole of season 4 is mostly lacking in animosity, especially compared to the cruelty displayed by both parties in the previous seasons, and this remark hammers that home. It's nice given that Sissi and the group were friends in the prequel before the misunderstanding that broke them apart happened, and it helps make it all the more understandable when they say in the final episode that they have already come to consider Sissi their friend now.
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. The best examples are "Hot Shower" and "Lost at Sea".
Crossed with a Crowning Moment of Awesome, in "Ghost Channel", X.A.N.A. has trapped Ulrich, Odd and Yumi in a virtual replica of the real world and has the means to erase them though they haven't figured it out yet. Just as X.A.N.A.-Jeremie has convinced the boys to go to Lyoko and almost convinced Yumi, the real Jeremie shows up. After some back and forth, Jeremie explains that he's virtualized himself. X.A.N.A. smugly claims that this proves he's the fake since, quote, "everybody knows that the real Jeremie would never virtualize himself; he'd be much too frightened"; Jeremie recoils in horror as it is true that he's terrified of virtualizing himself (rightfully so since the last time he did, he nearly got erased from existence). His friends exchange a brief glance and all 3 declare that there's no doubt in their minds that Jeremie would virtualize himself to protect them.
Also earlier in the same episode, despite his feelings being badly hurt by an insensitive comment by Odd, after the Return to the Past, Jeremie's completely forgiven Odd and is immediately very worried to find that Odd and Ulrich are both missing.
Jeremie: Aelita...there's something I wanted to tell you: I'd much rather enter a virtual world..to find you waiting there for me.
Aelita: *smiles* So would I.
"Code: Earth". All of it.
The fact that Jim becomes allies with the kids in the episode after learning everything the kids have done is awesome! Also the fact he ends up making it up for accidentally hurting Jeremie, which he is visibly upset about having done.
The entire episode was all for Jeremie could get Aelita back to the human world. And by the end, he does.
Jeremie: Welcome to earth.
The ending to "False Start". Despite the fact that she still has the virus inside of her, the group still insists that Aelita still come to the real world, despite the risk of XANA coming after her. They really care for her living at least once in her life not trapped in the virtual world. Considering how Season 2 shows her out of Lyoko and living among the others, it's possible she does.
The kids telling Principal Delmas how a good person Jim so he doesn't give him scolding for his usual paranoid behavior about them. Considering how Jim became their friend after the events of "Code: Earth" and "False Start", this is pretty heartwarming.