The opening to the first episode — Jaden is rushing to his academy entrance exam... and bumps into someone. At first you would be forgiven for thinking he was just an average bystander but then you realize it's Yugi, all grown up. After Jaden apologizes for bumping into him and explaining why he was in a rush, a GX remake of the original Yu-Gi-Oh! theme song plays and Yugi gives Jaden the Winged Kuriboh... a symbolic passing of the torch.
In episode 4, Jaden passes the test and impresses the headmaster so he he moved to Ra Yellow. He refuses as he doesnt want to be in a different class than Syrus.
Chazz's enrollment at North Academy. When he arrives, he meets a middle aged man who informs him that the requirement for entering North Academy is to find 40 cards in the arctic wilderness around North Academy. The man said he found 39 cards but doesn't have the strength to find the last card. Chazz heads off to gather his own 40 cards and when he returns gives one of his cards to the man so he wouldn't be stuck outside, especially since this would leave Chazz one card short. Considering this is before he turns over a new leaf, it shows that even at his worst, Chazz really isn't that bad of a guy.
Another from Season 1: Zane's big bro moment with Syrus right before he throws the duel with Camula to save Sy's life.
During Crowler's duel with Camula, she offers him the chance to back out without losing his soul if he'll let her duel one of his students instead, Crowler despite being scared of the shadow game refuses to back down, saying he won't let her lay a finger on any of his students and that she'll have to go through him first, also doubles as a CMOA.
Kaiba delivers one in his own aloof way in episode 35, by expressing his confidence in Chazz's victory despite the handicap he was issued.
Kaiba: Of course he won. Did you really think I would give Duel Academy to [his brothers]? They have a lot to learn about world domination...
Season 1, Episode 41: Alexis defeats Titan, restoring her brother's memory. The ending of the episode (before The Reveal anyway) is one big D'awwww.
The scene in Season 1 ep 47 between Alexis and Zane qualifies in both languages. In the original, Asuka thanks Ryo for being an older brother to her while in the dub Zane jokingly offers to be her bodyguard and then tells her he'll miss her when he graduates.
Crowler's duel against Chumley in season one also qualifies. If he could have let Chumley win, he would have, but it wouldn't have been fair like that. And he lets him go to his dream job anyway, because Chumley had proven that he earned it.
It was also one of the few times when Crowler was shown to be a professional. He dueled Chumley not solely to stop him from pursuing his dream, but rather as a teacher administering to a student a final exam to see if he/she was ready to venture out into the world. Despite the loss, Chumley proved to Dr. Crowler that he was able to make good decisions in both dueling and in life; and the duel itself was lost solely because Crowler had more experience than Chumley.
After Zane dominates the pro league with his new dark persona, Sheppard duels him in an attempt to turn him back to normal. He fails which results in Zane getting his hands on the Cyberdark deck. Sheppard then invites Zane to Duel Academy's GX tournament because he believes Zane can still be brought back by his friends. It shows how much faith Sheppard has in his students.
Crowler's duel against Bonaparte starts with Crowler on the receiving end of a Curb-Stomp Battle before losing his confidence. Jaden helps psyche Crowler up with a line from his lectures; keep in mind, Jaden sleeps through most lectures and yet still remembers Crowler's teachings, so this means a lot. Crowler then turns around and tells Bonaparte that a good teacher is one that learns from his students. If there's a scene demonstrating Crowler's Character Development, this is it.
The entire reason the two are dueling to begin with? Bonaparte wants the Red dorm torn down, but Crowler isn't having any of it. No matter how much he tries to deny it, Crowler has grown to care about them.
In the original, Crowler states his reason for fighting so hard to save the Red Dorm: as an educator, he believes that students of any ability should be allowed to develop their potential. It's acknowledged as a heartwarming moment in-universe, but is almost ruined by the fact that he's delivering the line through the pain of a Groin Attack by Bonaparte's monsters.
Tyranno Hassleberry/Kenzan's duel with Sartorius. Sartorius gives him a line about destiny being the reason dinosaurs are extinct, Hassleberry replies that dinosaurs live on through him.
Judai vs. Manjoume in Season 2. Manjoume breaks free of his brainwashing mid way through the duel thanks to the efforts of Judai and the Ojamas, who joined Judai's deck in order to help bring him back. He has no idea what's happening or why he's dueling Judai but first order of business? Get the Ojamas back to his side of the field and use them to defeat White Thunder's ace monster at the cost of the duel itself, which he was fully aware would happen. He even calls the Ojamas the aces of his deck upon getting them back.
Winged Kuriboh always helping Jaden. The most notable moment of their bond was when Jaden lost the ability to see his cards. The night the Neo Spacians helped him regain them, Winged Kuriboh gets the last but best treatment during the reunion.
A flashback of young Jaden drawing Neos on paper when Jaden says him and the Neo Spacians have a bond Sartorius could never understand.
When Jaden couldn't see his cards after losing to Aster and he leaves Duel Academy, while stuck out in the ocean he stumbles into Neo Space where he is greeted by a dolphin-like creature named "Aquos" (who is later revealed to be the spirit of "Neo-Spacian Aqua Dolphin"). After winning a Duel against an evil robot, Jaden rediscovers his love for Dueling and regains his resolve having obtained cards he drew as a kid from a Kaiba Corp contest. At the end of the episode, Jaden discovers his new deck has been infused with the power of Neo Space, and Aquos tells Jaden he can count on him as an ally and friend.
In Season 3, this same sentiment is repeated throughout the duel with the Yubel-possessed Johan. Judai's still dealing with remnants of his Heroic BSoD from his time as the Supreme King, and yet all of his monsters show up to prove that he's still the duelist they chose to follow, giving him the courage to keep fighting on.
During the final duel with Yubel, Aqua Dolphin echoes this again telling Jaden the Neo Spacians believe in him while dissolving his doubt, actively volunteering to be used as a sacrifice for Elemental Hero Prisma.
Sartorius apologizing to Aster that he used him as a puppet of destiny to escape his demise, but Aster tells him they really are friends and Aster really does want to save him from the Light of Destruction.
Jesse and Jaden's friendship. So many people look up to Jaden and put him on a pedestal, it's nice to see him have someone that's entirely an equal. And it appears that Jesse is choosing to dorm in the Slifer Red to hang out with him, rather than the nicer and fancier Blue dorm.
Any time Ruby Carbuncle and Winged Kuriboh start play fighting. It's pure Cuteness Overload.
There's a lot of warmth in the aftermath of the duel between Judai and Professor Satou, surprisingly considering this is Season 3. Judai's clearly doubting himself and wondering what he's dueling for and then Johan comes around, making sure Judai's okay. The viewer is then treated to one of the first scenes where Judai tries to reach out to someone, asking Johan what he duels for, and when Johan answers him clearly after a few episodes, you can tell it left a mark on him. Even when the dimension shenanigans go down, Judai tries to uphold Johan's example, dueling for others. It doesn't work considering the Supreme King, but the effort was there.
Shirley the Crocodile running up to shield Jim from the Supreme King's final attack.
The Crystal Beasts reaching out to Jaden, begging him to save Jesse since they can't and then later them and Jaden all calling out to wake Jesse up within the the Rainbow Dragon.
Jesse loans Jaden his deck for his duel against Yubel. The Crystal Beasts are his family, but he hands them over without hesitation, trusting Jaden to keep them safe. Even better when Jaden uses Rainbow Dragon against Yubel since the Crystal Beasts won't let anyone but Jesse use them.
Jaden using Super Polymerization to fuse his spirit with Yubel's to keep his multi-lifetime promise to always be together. Yubel even breaks out in tears. The speech that Jaden gives Yubel before their spirits intertwine about his intention to soothe their damaged mind is particularly heartwarming.
At the beginning of the Season 4 episode, when a meteor crashed into the forest, Syrus finds Jaden in one piece and tearfully runs over with outstretched arms to hug him.
After the duel when Syrus defeats the Psycho style duelist, Zane gives his Cyberdark Deck to him, complementing his use of the deck while admitting he's inspired to build a new deck and chase after his younger brother in the pro league.
Manjoume, in his duel with Edo, declaring a direct attack with Ojama Yellow. Ojama Yellow hesitates for obvious reasons (attack: 0), but Manjoume reassures him he's the ace card of his deck. He then plays a combo that wins the duel.
In his duel with Yusuke, Fubuki doesn't care about what Yusuke is doing, he's just glad his best friend is alive, and apologizes that he didn't save him the first time.
Throughout season four, it seems that Jaden may never return to being his original happy persona. Thankfully, Winged Kuriboh induces some very convenient time travel, so that Jaden can face his idol: Yugi Moto, the King of Games. This duel rekindles Jaden's passion for dueling and returns him to his old, duel-loving self.
Most importantly, when fighting Jaden, Atem's spirit comes out to duel him and unleashes Slifer on him. Not because of a threat or how important the duel is, but because Atem senses such a strong duelist that he wants to test his abilities himself. Probably the highest honor he can give to Jaden.
The aftermath of Jaden and Alexis' tag duel in the final season. Alexis can't quite confess her feelings but they have a sweet heart-to-heart conversation. To cap it off, Jaden gives his signature "Gotcha! Nice duel!" gesture; Alexis had been wanting to see him smile again and finally got to see it.
Crowler and Jaden's season four duel. From wanting to get Jaden expelled in the beginning, three years earlier, Crowler now fights to keep him, and all of his friends in the school instead, not wanting them to leave him. It mirrors that first duel, right down to the monsters they played back then, and the entire school is cheering for them both to win, even though if Crowler does, Jaden's whole class will be held back. Crowler's inner monologue makes this all the more touching, as he notes that he still secretly hopes Jaden will find a way to overcome his most powerful deck.
The final turn is important too as the events brought out Crowler's Ancient Gear Golem facing off against Jaden's Flame Wingman with the Skyscraper field in play and the remainder of the duel plays out the exact same way as when Jaden defeated Crowler the first time. With it he sees flashbacks of the drop out boy who had hopes to enter his dream school and will soon graduate and leave, finally admitting how much Jaden and his class taught him as much as he taught all of them.
Also, for season four: when Jaden duels Nightshroud, and Nightshroud yanks Yubel out of Jaden's deck/soul and forces her to attack his monster. Due to Yubel's special effect, that would cause Jaden to lose the duel. But he plays a card so that she attacks him directly (Yubel has no attack points, so no damage is caused). What's heartwarming is: he catches Yubel's fist, folds his hand over it gently, and tells them that he'll take them back, no matter what.
Judai finding the farewell letter in his bag from all of his friends in the final episode. Even after everything that's happened, they still love him, and Judai loves them too.
The last scene of the manga, in which Koyo has awakened from his coma, and is facing Judai in a duel as he promised.
Also in the manga, in which, after Syrus loses to Chazz, Zane repeats his question of whether he wants to become a duelist. Rather than give his statement that he wants to "be" a pro duelist, which prompted Zane to doubt his resolve, Syrus says he wants to "fight as" a pro duelist, impressing Zane.