Judai finding the farewell letter in his bag from all of his friends in the final episode.
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 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.
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 have caused Jaden to lose the duel. But he played a card so that she attacked him directly (Yubel has no attack points, so no damage was caused, thus her special effect was invalid). What's heartwarming is: he catches her fist, folds his hand over it gently, and tells her that he'll take her back, no matter what. *bawls just at the thought of it*
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.
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.
Another from Season 1: Zane's big bro moment with Syrus right before he throws the duel with Camula to save Sy's life.
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.
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.
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.
During the final duel with Yubel, Aqua Dolphin echoes this again telling Jaden the Neo Spacians believe in him while dissolving his doubt.
Crowler's duel against Bonaparte. Jaden boosts Crowler's confidence when he starts losing, Crowler then tells Bonaparte that a good teacher is one that learns from his students
After the duel when Syrus defeats the Psycho style duelist. Zane gives his Cyberdark Deck to Syrus, 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.
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.
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.
Shirley the Crocodile running up to shield Jim from the Supreme King's final attack.
A flashback of young Jaden drawing Neos on paper when Jaden says him and the Neo Spacians have a bond Sartorius could never understand.
In his duel with Yusuke. Fubuki didn't care about what Yusuke was doing, he was just glad his best friend was alive, and apologized that he didn't save him the first time.
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.
Jaden using Super Polymerization to fuse his spirit with Yubel's to keep his life time promise to always be together. Yubel even breaks out in tears.
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 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 isn't all bad.
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.
This far and no mention of 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.... the voice reveals 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 and it touched the heart of this troper.