In Asatte no Houkou the flashback in episode 8 was very touching. Little Karada clinging onto Hoshi and crying 'Onii-chan' with him answering 'Hai' every time after their parents death. Well, actually most of Asatte no Houkou. It's a very heart-warming series.
While Asu no Yoichi is alight with moments of awesome, funny and heartwarming due to the nature of the manga, this one (and that whole chapter) really outdoes the others.
After rescuing Miyako and pacifying the spirits, the sky clears and the cast gathers together in a happy final scene with all of their problems neatly resolved in Ghost Hound.
It's kind of subtle, but before that, when Taro is in the hospital and Makoto is having family troubles, Masayuki is the one who goes and spends some time with them. Later he helps rescue a classmate from bullies. This doesn't seem like much until you remember Masayuki's backstory. He is trying so hard to start over and be a good friend, despite his own issues. It's sweet.
The ending of Gunbuster: Noriko and Kazumi return to Earth after 12,000 years, to see that everything is dark, and wonder if the human race ended up being wiped out after all... and then the Earth lights up into a giant "Welcome Home" sign.
When Henrietta seemingly shoots herself and Jose desperately tries to stop her. She then reveals that she used a blank round and says that she'd never kill herself while he loves her as much as he does.
In Initial D, the dog-kicking, dirty-playing Jerkass road racer Shingo suffers a brutal crash after an attempt to wreck Takumi's Eight-Six in a race. Iketani and Itsuki come across his wrecked car, and despite the fact that the former almost had his car wrecked (again) by Shingo and the latter had a date broken up because Shingo wrecked his car, the two offer to escort him to a hospital in their car.
Junjou Romantica is packed full of these, but my personal favorites are when Miyagi takes Shinobu to his first love's grave to tell her that he has fallen in love again, when Hiroki sends Nowaki flowers and when Misaki finally, finally manages to tell Usagi that he loves him.
In Kamichu!, Yurie has to find the couple who once were regular visitors of a now-abandoned beach - and later she finds out that they are her own parents. The sweetest part is when she transfers her divine power to them by kissing them on their foreheads.
What about episode 15, probably the most heartwarming episode in a series made of nothing BUT heartwarming, cute, and fluffies. On Valentine's Day, THE ENTIRE TOWN, humans and gods, apparently all know about Yurie's crush on calligraphy club-president Ken-chan (except for Ken-chan) and all of them, particularly the women-folk, support her and help her to confess her love to him on the big day. Yurie's friends help her make chocolate; on her way to school, she has old ladies wishing her luck and telling her to do her best; her classmates subtly gossip around Ken-chan about how cute, helpful, and popular Yurie is; Mitsue and Tama bring Yurie the chocolate when she forgets. When Yurie approaches Ken-chan on the roof she gives him the chocolate and admits that she always loved him, and asks him out. Ken-chan exclaims "So that was it! Why didn't I realize it before?" He writes the calligraphy for LOVE with a mop on a giant piece of paper and says that he just realized he loves Yurie too. Then Yurie's kamichu powers kick in and they fly through the air on the sheet of paper that says LOVE like a magic carpet.
A sweet one is in episode 6. Yurie is suffering from a fever, and receives a get-well charm. It has an odd effect on her, causing her to leave her body and float through the town. She uses it to check up on everyone, and her love interest Ken. Since no one can see her, she just sits next to him and watches him with the most adorable smile on her face. As she gives in to herself and reaches out to touch his cheek, he turns suddenly and sees her, startling Yurie back into her body. And later on this CloudCuckoolander who can barely remember her name sends her calligraphy of a get-well charm, saying her face appeared to him as he was doing it. Out of everyone he was the only one who could see her.
Every episode has, at least, one of these. Even if it's not very strong.
Prince of Tennis has two memorable ones. Like when the first thing Eiji went to after his match against Higa was his doubles partner. But it doesn't compare to the Anime's season finale, where Ryoma ends up using all the signature techniques of his teammates to defeat Tezuka so he can move onto the US Open, saying thank you to each of them when he uses their move. Oh yeah, and Ryoma was crying during that portion with him finally saying "Thanks for everything...".
Episode 51 of the Kirby anime is one big Crowning Moment Of Heartwarming for every character. Except possibly Dedede and Escargon.
Fumu: "Everyone loves you, Kirby!"
In the second episode of Kurau Phantom Memory, Kurau suddenly grabs Christmas and takes off into the air with her, after Christmas says she wants to be able to fly as well. The imagery of Kurau happily holding her long-awaited "pair" while flying over the city and Christmas' cheery response is a pleasure to watch — but also quite foreboding.
The end of the first episode, when Christmas appears and Kurau quietly weeps with joy.
As might be expected from the title, Mahoraba ~Heartful Days have many moments like this, but the best one comes in the climax of episode 22.
The Maoyuu Maou Yuusha adaptation "Kono Watashi no Mono to Nare, Yuusha yo" "Kotowaru!" has one in chapter 15, when Maou/Demon Queen is being mental assaulted by her ancestors. She resists by telling them they can't have her, she already belongs to Yuusha/Hero. Then she describes his hair to illustrate their bond.
Minami-ke's tedious and mediocre second season (Okawari) redeems itself somewhat with the unexpectedly well-done last episode, in which Kana and Chiaki plead with their older sister Haruka not to study abroad, leading to a warm (although somewhat clingy) display of sisterly love.
And then some familiar music comes in — and you realize it's the first season theme. Even if you like Okawari, it's a satisfying callback.
Najica Blitz Tactics, mostly being a fanservice-overloadedpanty shot vehicle, actually pulls off a very sweet scene in which android Lila closely observes Najica's changes of posture and mimics them, just like a child would do - or perhaps a lover. It's just so darn cute, which also gets commented on by one character who watches this.
Lila does a lot of that. My favourite is the hilarious bit where she drops a plate and the noise shocks Najica into realizing something, for which she says thanks — so Lila starts dropping all the other plates one by one. Her childlike behaviour and bond with Najica are the real selling points of the show.
ROD the TV has a very touching moment when Hisami finally decides to say farewell to Anita before she moves back to Hong Kong. Their relationship was sort of an island of normalcy in Anita's crazy life, so it's quite chilling when in a later episode Hisami doesn't even recognize Anita anymore.
Wendy and Joker's ending
Did the scene in Nenene's apartment after Anita and Michelle found out about their fake memories when Anita starts crying on Maggie's shoulder.
How the three sisters met was heartwarming to the MAX. Even if it WAS fake.
And any time there's a Three Sisters Vote!
In particular, the one in episode 11 (IIRC): all of the votes in the early episodes are for comic relief, but it comes as a Meaningful Echo when they vote unanimously to rescue Nenene even at the risk of their own lives.
Revolutionary Girl Utena: The game of badminton between the Duelists. Especially this might be the last time any of them see Utena. And: "Wait for me, Utena."
The scene in the movie, when Utena says her farewells to the drowned Touga in the elevator.
Saikano has countless heartwarming scenes between the tearjerking scenes, most notably the end of the first half of episode 1 when Shuji and Chise agree to give love another go, the end of episode 10 when Chise finally returns to Shuji and they run away from their unhappiness together, and the first half of episode 11! (It can't last.)
The very, final end of the show, after The End of the World as We Know It when Shuji finds Chise and "enough of [her] is in his heart" that she can become 'real' again and they can live happily ever after.
In the final ep of Samurai Pizza Cats tough-as-nails Polly Esther breaks down when she realizes that Speedy- who she usually yelled at for goofing off or being slow delivering pizzas- is risking his life to stop a comet from crashing into Tokyo. The thought that he might not come back alive finally leads her to look beyond his faults and admit her feelings at last, crying out loud, "I love him so!" Awww!
The 3rd part of the 5th episode of Shinryaku! Ika Musume, titled "Won't You Keep It?" The segment manages to end on a Tear Jerker, but that doesn't change the fact that the rest of the story of Eiko and Mini Ika is a complete and utter joy to watch.
In the manga version, Marron's flashbacks of Carrot saving him from bullies, and how that inspired him to become the person he is today. Also, Chocolat's two-volume flashback explaining how she and Tira came to live with Carrot and Marron's family and why Carrot means so much to her now.
Chris Thorndyke may have annoyed 80% of the viewing audience but the end of the second series of Sonic X and Sonic takes him running one last time, before he has to do the whole return to his own world forever thing. It's summed up in the fact that Sonic cries for the first time ever in that continuity, and the kid gets the tears in his face. That you never see Sonic's eyes just makes it worse.
Similarly, in Sonic X, Cream's reunion with her mother.
Sonic X again. During the episode Last Resort, Amy makes Sonic a bracelet out of shells to protect him when he's around his weakness, water. Instead of being all put out the way he usually is when Amy makes a romantic gesture, Sonic can only stare at her in surprise. The look on his face, coupled with the look on Amy's, is absolutely adorable.
Add this to the fact that after the bracelet is smashed , and Amy is convinced it's lost, the episode ends on a scene with Sonic, watching the water and wearing the repaired bracelet. Awww.
The ending to Episode 52, Memories of the Wind. There Amy has waited for a good while for Sonic to return. When he does, Amy rushes to him, yells at him while in tears, then finally declares she would have waited for his fateful return for the rest of her life. THEN she screams for Sonic to just tell her he loves her. Sonic responds by giving her a flower and an answer...which is inaudible and thus ambigious. But it works so well.
In the Japanese version, Chris had to make the difficult decision of letting the others use the Master Emerald, in order to help fight Dark Oak, which would most likely prevent the kid from ever returning to his own world, and in distress over it, despite shaking it off and smiling like it's nothing. Decoe, Bocoe, and Bokkun respond by telling him that there's nothing to worry about, how their galaxy is fun, and offer him to join them and Eggman- just being welcoming and supportive of the kid. They might have been joking and trying to humor Chris, in order to cheer him up(and it looked like it partially worked, too, judging by Chris' response). But it was nice to see Character Developing in not only Chris, but in Decoe, Bocoe, and Bokkun, as well, and how it appears that they have grown something of a soft spot for Chris over the course of the series.
The Stoic Meia comforting newcomer Misty in Vandread and caring for Ezra's baby Karu (AKA "Pyoro II").
Later in the series Bart befriends a Littlest Cancer Patient named Shirley, whom makes a small felt doll in his likeness, but who dies before she finishes the hair. At the end of the episode, we see that Bart has shaved himself bald to match the doll.
There's also a storyline in an earlier volume where Kyohei is forced to stay in the hospital and makes friends with the spirit of a beautiful young Bishounen trying to find a hidden love letter he wrote for his sweetheart years ago. With help from Sunako and Kyohei, the ghost finds the letter and gives it to his aged sweetheart, who is Kyohei's nurse and a very touching moment is felt. However, the reunion is sadly cut short when the ghost passes on over to the afterlife.
And the final strip: Alpha goes into Yokohama for coffee beans, just as she did in the first strip, and comes home to find Kokone there waiting for her. So very, very sweet.
The whole damn series. Which is odd, because it takes place After the End.
The very last scene in the final TV episode of Jungle wa Itsumo Hare nochi Guu. Despite the rest of the episode essentially being as nonsensical as the rest of the series.
Sister Princess: At the end of episode 20, when, as a Christmas present, the sisters sing a song for their brother. An example of Crowning Music of Heartwarming.
The very final scene of Vision of Escaflowne has Hitomi back on Earth after her adventures on Gaia. She briefly sees a vision of Van smiling in at her and wearing the pendant that she gave to him before she went back. She smiles and says, "I'm doing fine."
Ifurita: "This is destiny, Makoto. If I had not undertaken this journey, I could never meet you, and that is why I am going...to meet you - because I had nothing until I met you, not even a single memory."
Makoto "Then let me give you mine." [A Montage of Makoto's memories on Earth with Ifurita placed in them, at peace and happy, follows]
The final scene where Ifurita is all alone in the schoolyard, seemingly forever trapped out of her world and time. Suddenly, a slightly older Makoto materializes with her key staff as promised to rescue her and she joyously runs to join him and go home to the tune of a beautiful ballad.
The end of the final Episode of Abenobashi Mahou Shoutengai: Sasshi says Screw Destiny, finally renounces being a kid and wants to grow up for Arumi (meaning he'll face that they'll move away and that he'll lose his old environment) and changes all of reality to not only bring Masa-jii back to life but also to resurrect Mune-Mune and Abe no Seimei to live the life together they had wanted.
In Piano, Miu plays a waltz by Chopin for her friend Yuuki and gets her feelings across. It's actually quite rare that Miu performs a whole piece for somebody, even though the show is supposed to be about her piano playing.
In Kill Me Baby, the comedy is based mainly around Yasuna annoying Sonya, usually resulting in Sonya hurting her. However, in Episode 13, we see that the two really do care about eachother.
Haru wo Daiteita: When Iwaki declares his love, he entwined his fingers with Katou and held them to his heart.
From the Street Fighter manga Sakura Ganbaru, Sakura's father discovers his daughter's dangerous hobby and says "When I first saw it, I thought 'I won't allow this', but to see your child throw themselves into something so earnestly... No parent would want to discourage that..."
Girls Bravo: Kirie hugging Yukinari and encouraging him to go rescue Miharu.
My Last Day unfolds through the eyes of a thief who receives the same brutal crucifixion sentence as Christ. Later, when he and Jesus have died on their crosses, we pan up to Heaven and see the thief with Jesus who recites John 11:25.
Hyperdimension Neptunia The Animation has a few (what with the adorable nature of nearly every character) but one stands out. After the fight with Arfoire and all the CPU's are freed, you see the little sisters hugging their big sisters...with Vert being left out. Cue Nepgear walking over to her and giving her a nice big hug to show that they missed and love her too.