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YuYu Hakusho is a series focused on an emotionally challenged angry boy and generally doesn't lend itself to these, but when they show up, they are especially poignant.
Two such moments occur during the Dark Tournament arc. The first occurs toward the end of Yusuke's final test, absorbing the Spirit Wave Orb. He has spent a long time in absolute agony as this energy integrated itself in his body, and Puu, his spirit beast, has been suffering the same torture. In time Yusuke starts to run out of strength, and gives up, resigning himself to die. Suddenly, he's pulled back by a splash of water on his lips, and he opens his eyes to see Puu flying off again to fetch more water in his wings. Puu is obviously in pain, even as he does this, and as he shuffles back to Yusuke, he trips, spilling the water all over. It only gets worse (or better) when Puu just stands back up, and goes for more.
Not moments later, Puu trips again, but this time, a large rock dislodges from the ceiling, threatening to crush and kill Puu. At this Yusuke stands up, and rushes over, blood still bursting out of him. In a particularly heartwrenching cry of "Screw this test! I'm getting us out of here!" he smashes the boulder, saves Puu, and integrates the orb into his body in one swoop. This is also a Crowning Moment of Awesome.
Another moment comes some episodes later, during the final showdown with Toguro. Toguro is frustrated with Yusuke's inability to reach his full power, and declares he will kill one of his friends if he doesn't do it on his own. Toguro chooses Kuwabara. Though said death is later subverted, as Toguro and Kuwabara both realized Yusuke only needed to think Kuwabara was dead.
And finally, at the end of the series, in the wrap-up episode where we see what everyone has been up to after this all finishes up, all the characters, minus Yusuke, find themselves at the beach, enjoying themselves. Keiko stares out at the waves, and finally declares that she can't wait for Yusuke anymore. Of course, it's at that moment that Yusuke shows up, saying she doesn't have to anymore. Long story short, they kiss. Finally.
At the end of the manga, Yusuke is forced to choose between three buttons that'll either A) Shut down a cults doom cannon, B) Fire it or C) Self detonate it, killing him for good as he's already in a spirit form. The cult is obsessed with the number three, and tell him that he'll only guess the right button if he has their god's blessing. After a long think, he chooses the blue button, as it's Keiko's favorite color. As he puts it; "They've got their god, I've got my goddess". When she finds out how he chose, they have a different touching beach moment.
There's also the scene where Mitamura reunites with his three students after he's been cured of his terminal illness and they've been released of the mind control they were subjected to when they agreed to become Ichigaki's guinea pigs in order to cure him. What almost became a great tragedy has a happy ending.
Mitari/Seaman's Heel-Face Turn. Even though he tried to kill him, Kuwabara still saves Mitari's life, which makes him question the Mind Rape induced view of humanity that Sensui subjected him to. In the end, when Kuwabara is kidnapped by Sensui, Mitari begs Kurama and the others to let him help them "if it's not too late". Kurama then extends his hand and tells him that it's never too late to make a new start.
There's a example in the manga chapter "Special Day." Hiei goes to talk to Mukuro, and tries to get her to admit her father sexually abused her. Mukuro kind of knows he's right, but her memories have been altered so that she remembers her father as loving and kind, however, so she punches Hiei through the roof. Literally. Undaunted, Hiei goes to visit Kurama, gets another plant like the one that is trapping Toguro-ani, and traps Mukuro's father in it... and pots it, presents it to Mukuro, tied up with a bow, as a freaking birthday present. And wishes her a happy birthday. Obviously, you do not want to be on Hiei's bad side. It's their smiles that make it a CMOH, because otherwise... brrr.
Their fight in the anime is exceptionally poignant, especially in the end, where Mukuro wins by stopping the Dragon of the Darkness Flame, and the two share a conversation about breaking away from the past at long last. A weakened Hiei then collapses, Mukuro catches him, and the stern facade that they both have melts away as they embrace. Considering the type of person Hiei is, this is highly noteworthy Character Development. The soft piano music that plays in the background makes things even more heartwarming.
Kurama's selfless love for his mother, especially during his last fight in the Three Kings arc. Aside from keeping in touch with her by phoning her from Makai, he undergoes a dilemma in which of his lives to give up. With the memory of a sakura tree in their back yard, he manages to defeat Shigure and move on with his life in the human world. Afterwards, Yomi helps him get back to his feet and a two-sentence conversation singlehandedly defines Kurama's character arc:
Yomi: "Kurama... have you forever forsaken yourself as Youko?"
It goes the other way too. In a later episode, a bully holds Kuwabara's cat hostage to force Kuwabara to do things that break his honor code. One of those things was for him to beat up his friends, which Kuwabara refuses point-blank to do. His friends tell him it's fine and urge him to do it, saying they won't hold it against him and instead will just see it as the bully being the one to attack them.
Yusuke helping Kuwabara study for the exam as part of a condition made by Mr. Akashi to help protect Okubo's part-time job by entering his dreams.
All of the anime episode "Kurama's Secret!? The Ties Between Mother and Son." After defeating Goki and freeing all the souls that were eaten by him, Yusuke meets the mysterious Kurama, the guy who possesses the Forlorn Hope. Which by the way is an artifact that enables its user to have any wish they want, at the cost of their own life! Yusuke finds out that Kurama only wants to use the artifact to save his human mother, at the cost of sacrificing himself. Yusuke, believing that Kurama's sacrifice would cause his mother to suffer, offers to give his life to the mirror instead so that Kurama wont have to die and leave her alone. In the end, the Forlorn Hope takes direct action and willingly spares both of them. Awwww!
When Keiko's running through the fire in Yusuke's house to save his body, he tries telling her to leave. The investigator reminds him that if she doesn't save his body, he won't be able to come back to life. He screams at her, "What's the point in coming back to like if Keiko has to die for it?!"
Yusuke's wake is an odd first episode example. A 14 year old kid goes from seriously believing that the world and everyone around him would be better off and not wanting to come back to life to wanting to try and live again after seeing how his mother, love interest, teacher, and rival all act.
During the fight with Yomi, Yusuke's Heroic Second Wind which has him get rooted for by every major character in the series everybody shows up Kuwabara, Kurama, Hiei, Genkai, Botan, Koenma, George, Chu, Jin, Toya, Rinku, Suzuka, Yukina, Shizuru, Puu, Kaitou, Kido, Yana, Hokushin, and The Monks before finally Keiko appears this causes Yusuke to tap into Sacred Energy. It has to be seen to be believed.
Yusuke aimed to shoot Bakken from behind, risking the consequence of throwing away the whole tournament just to save Kurama.
Also, Hiei. During Kurama's fight with Bakken he was about to throw away the tournament and waste the chance of healing his crippled arm (the barrier keeping him out of the fight was also healing his crippled right arm), and when Kuwabara was about to lose against Risho he was preparing to break the barrier and throw away the tournament (only that, as the arm was now healed) to save him.
Kuwabara and Kurama conversing at the start of the final episode is a nice little treat, as the latter shows a bit of pride in seeing how far Kuwabara has grown as a person in the last 2 years, whereas Kuwabara indignantly defends Kurama when 2 girls are convinced the latter is either a girl or Kuwabara's boyfriend.
Quite a bit before this, in Episode 101, we see Kurama narrating what is was like being at his mother's wedding, stating that it was a quiet affair, with only family and close friends attending. As he's telling us this, we see that Kuwabara was standing right next to Kurama at the wedding, showing just how deep the latter regarded their friendship.
After Yusuke arrives to Yomi's territory (following Raizen's death), the viewers are treated to the sight of Kurama and his trained recruits waiting in the room adjacent to them, ready to possibly intervene and/or attack Yusuke on Yomi's orders. However, their reactions to his arrival are hardly antagonistic. Jin and Chu are ecstatic to see Yusuke again, noting his increased strength with admiration. Kurama then notes his reluctance to kill Yusuke on Yomi's commands, and asks the rest what they think. Chu, Jin, Rinku, Toya, and Suzuki instantly respond that they would side with Yusuke over Yomi (with Rinku even plainly adding "Do you even have to ask?"). When Shishiwakamaru expresses indifference, Suzuki is quick to override his vote by stating he'd be on Yusuke's team, as well. And Kurama follows through on this immediately afterward by supporting Yusuke's tournament plan.
When the group reveals itself, Yusuke is similarly happy to reunite with his former rivals. He, Chu, and Jin even grapple their arms around each other and start laughing joyously.
The laugh Hiei gives after hearing Yusuke's tournament idea is a bit of this in itself, with him taking glee in knowing his old ally was able to outsmart Demon King Yomi.