There was a single issue dealing with Tim Drake after his father had been killed in Identity Crisis. Taking the Batman route, Robin shuts his feelings in and tries to act cheerful (ending up being more cheerful than normally), and only Conner really knows what's bothering him and encourages him to talk to the team about it, which Tim still refuses to do. Later, when they are chasing Electrocutioner, said villain begins making father-insults to Tim (mainly alluding Batman as Robin's father, since he does not know the boy's identity), which causes Robin to beat him to a pulp in a sudden rage before the other Titans stop him. When he finally tells them what's wrong and Wonder Girl asks if he wants to talk about it, he hesitates before looking at them with tears in his eyes, muttering "Yes. Yes, I think I need to." We then close the issue with a panel of Robin being hugged by Wonder Girl, with all the Titans there for him and these words:
Robin: For the first time in a week, I stop thinking like Batman. And I start thinking like a Titan.
During the Dark Side arc of Teen Titans, Kid Devil goes into an Unstoppable Rage and almost kills a brainwashed Hardrock, venting out out a great deal of pain and frustration from being seen as the weakest link of the team, beaten up, tortured by Clock King and told that no one loves him in order to condition him into a monster for fighting in the Dark Side Club. Miss Martian gives Eddie an "I Know You're in There Somewhere" Fight speech with her telepathy to bring him to his senses.
M'gann: Eddie. No. Eddie, Please Listen...This isn't you. You're not a killer. What they did to you—what Clock King said to you... None of it's true. You're not a monster. You're not alone. You're not unloved. You're a sweet boy who had a dream to be a superhero sidekick and got to live that dream. You're thoughtful, funny and earnest. You're a Teen Titan, Eddie. You're a good guy.
This scene, where the original five Titans — Dick Grayson (Nightwing), Donna Troy, Garth (Tempest), Roy Harper (Arsenal) and Wally West (The Flash III) — run across statues of them from way back when they were teenagers — as Robin, Wonder Girl, Aqualad, Speedy, and Kid Flash. They comment that even though their lives have taken so many twists and turns since the '60s that it's a miracle they're all alive, they are still together, still friends, and still Titans.
Basically any time Roy Harper is together with his daughter Lian it is bound to make a reader go "aww" or start crying.
Teen Titans: Year One, the modern look on how the original five founded the team, ends with Batman at his computer, trying to think of something that will convince Dick to come back and continue to be his sidekick. After multiple attempts with lengthy, emotional sentences, he settles on three simple words. "Robin, come home".
In the crossover with Red Hood & The Outlaws during Death of the Family, which saw the Teen Titans teaming up with the Outlaws whilst trying to find Red Hood & Red Robin, Bunker & Arsenal are left to fend off Jokerized civillians whilst the rest of the team races to get a cure. During the fight, Roy's inner monologue pays a glowing endorsement of the Titan.
"You watch, he'll be in the Justice League before he's twenty."
In another comic, Beast Boy gets one. He morphs into a parasitic worm, swims his way down into Brother blood's intestines to retrive Raven's chakra and back up again. He then later admits to Raven herself that he'd do it all again in a heartbeat for her. A very disgusting moment too yes, but still heartwarming nonetheless.
In "Raven Reborn" after Raven was freed from both Brother Blood and Trigon's influence, she begins to experience emotions that she has long suppressed. The main one being love. In an issue prior to this one, she inadvertently uses her powers to make Nightwing fall in love with her, when she thought she was in love with him. When Nightwing starts slowly catching on, she let's Starfire, who was dating him at the time know what happened. Rather than get mad, Starfire talks to Raven girl to girl, taking her to Tahiti. She helps Raven understand what she did to Nightwing was wrong and Raven in turn asks Starfire to help her understand these new emotions. After that's resolved and she and Starfire prank Nightwing, Starfire learns to her excitement that Dick wants to move in with her. As if that isn't heartwarming enough, after the return home, she went to Cyborg's home, the latter hosting a BBQ for the Titans. Because she arrived, she thought he was hosting a private party and didn't think she belonged there and left in a haste. Upon returning home, she listens to a message Cyborg recorded prior to her trip with Starfire, showing much to her excitement and embarrassment, that she was invited as well and assigned to bring pop, prompting her to come back and enjoy the festivities.
Roy and Lian helping Damage in Titans #17-19, after learning Damage's foster father repeatedly sexually abused him is this and a Tear Jerker. Roy brings the younger Titan with him and Lian on a camping trip in Arizona because he could tell Grant was feeling depressed after attending a trial for his uncle, Doctor Polaris. In a heated moment Grant blurts out his foster father used to hurt him and all but flat out says he was molested. Roy reacts to Grant's admission with horror and empathy while trying to make sure Lian doesn't get hurt because Grant's volatile emotional state might cause his powers to erupt. The two Harpers relate to Grant stories about the Navajo and how they deal with grief, and Roy has Grant direct his anger towards him so Grant can finally have an outlet to express all the pain and self-loathing he's felt. Instead of ending it there, Roy brings Grant to Oljato, the Navajo reservation Roy grew up, because it will give Grant a space where he can finally work through his anxiety and trauma without feeling self conscious about being around people he knows. Grant stays there for the rest of the series. The entire situation is a refreshing example of how abuse-related trauma should be handled, and at the same time demonstrates how much Roy has grown as a person after all the neglect he went through, and the perceptiveness Lian has developed despite being so young.
Damien sacrifices himself to try and have his team spared. In return, the other Titans come to rescue him from his Grandfather and Cousin.
The final scene of "Sisters", when Robin and Starfire are sitting watching the sunrise together and Robin tells her that, while her sister was interesting, "No one could ever take your place."
Before that, the fact that he, a completely normal human teenager, latches onto the bottom of an alien spaceship and engages two huge and heavily armed guards in order to rescue her.
What no mention of the "date" on the Ferris Wheel that begins the episode? It's little more than Robin explaining to Starfire how festival's go but it's just so sweet. Try not to melt when Robin is amazed by the fireworks and Starfire opines that "Earth is full of amazing things" while looking at Robin with glistening eyes.
Cyborg talking to the kid with the prosthetic hand in "The Sum of His Parts" twice. In the first encounter, Cyborg is depressed because he has to run to the Tower to recharge and miss a fun day barbecuing, and he doesn't seem to realize how excited the kid is at seeing his hero, or how excited the kid gets when Cyborg runs off to "kick butt". The second time, when the kid brings his friend to meet Cyborg, Cyborg not only tells the kids that it's what inside that matters that makes them Not So Different rather than the prosthetic, but also plays football with them! That kid probably had the best day of his life, playing with his "hero" and being told You Are Better Than You Think You Are.
On a meta example, show writer David Slack said that he got a similar message from a mom whose kid had a similar prosthetic, and was "like Cyborg." Representation matters!
Beast Boy: You think you're alone Raven... but you're not.
And to top it off: in response, Raven opens her bedroom door...and gives him a great, big hug (which is so unusual and OOC for her that Beast Boy is actually rendered speechless).
In "Apprentice Part 1", after Slade has blackmailed Robin into working for him:
Slade: "You'll grow to like this. I may even become like a father to you."
Robin: "I already have a father." *images of dozens of bats appear in the scene dissolve*
Keep in mind it's heavily implied in "Go!" that the last time he saw Batman they'd had a falling out and were no longer on speaking terms. Yet he still considers Batman like a father to him.
At the end of "Apprentice Part 2", when Robin softly admits to Starfire that he and Slade really are very similar. But also that there's one big difference between them: "Slade doesn't have any friends." Then, Robin smiles at Starfire before looking over at the rest of the Titans, who are being their usual, lovable selves.
The end of "Aftershock, Part 2", when the dust settles after Terra'sHeroic Sacrifice and life returns to normal, the Titans are seen carrying a plaque and flowers to the statue that was once their friend. It's hard to tell which part of the sequence tugs at the heart more; that or Beast Boy's speech, which mirrors and subverts the evil speech Terra gave at the start of the episode:
Beast Boy: "Her name was Terra. She was gifted with tremendous power, and cursed with it as well. She was a dangerous enemy, and a good friend. And she was one of the bravest people I have ever known."
Or when the team has made their promise to bring her back, and we see what the plaque reads:
Terra: A Teen Titan. A True Friend.
During the battle with Trigon, Robin is carrying the 10 year old form of Raven on his back, reminding her of why they are friends and how important she is to the team and to him.
Robin: Yeah. It's the end of the world. But so what? We're still here. Still fighting. Still friends.
Raven: Look at me, Robin! There's nothing I can do! There isn't any hope!
Robin: Then I guess I'll just have to have enough hope for the both of us.
Followed when Raven, now her right age and white outfit, takes down Trigon.
Starfire: Raven, that was...
Raven: No. It wasn't. (Robin comes up to Raven, and she hugs him tightly)
Raven: Somebody believed. (Robin puts a comforting hand on Raven)
Robin: Welcome back.
Don't forget at the end of "The End" where Robin tells Raven that her battle against her own demons and her destiny has always inspired him.
Beast Boy demonstrates a surprising amount of wisdom in an encouraging speech to Cyborg in "Overdrive", after the former has worn out the chip he implanted in his brain and is discouraged about failing to catch a criminal.
In "Fractured," Johnny Rancid gets Larry's powers and begins unleashing havoc. Robin doesn't even try to stop him because he worries he'll mess up again and make things worse. Larry, however, tells him this:
"I mess up all the time, but I still try. That's how come you're my hero, Robin. Because no matter what, you always try."
The end of "Lightspeed": As random as it might have been, the writers manage to make a lot of Kid Flash and Jinx's interactions pretty cute, starting from how when he first takes the Hive Five by surprise during a museum robbery, KF pulls pranks on all of the other Hive Five except Jinx, whom he gives a red rose. After Jinx's High-Heel–Face Turn, she has a rather unsure expression, but she stops in her tracks and finds another rose. After briefly spotting Kid Flash overlooking her and dashing away, Jinx walks ahead with a sweet smile.
His line about why he's bothering with her is also touching.
During the origin episode "Go!", Cyborg comforts Raven, who feels alienated after Beast Boy gets creeped out by her powers:
Raven: I don't exactly fit in.
Cyborg: He's green, half of me is metal, and (Starfire's) from space. You fit in just fine.
Doubly heartwarming considering the first time we see his cybernetic parts it's pretty clear he hates them, but Cyborg uses them in his example to make Raven feel better about herself.
"Car Trouble" is a good early one for Raven. She makes it plenty clear that to her "it's just a car,", but partway into the episode reveals that she does understand how Cyborg would be attached to his car the way he was, and at the end when rebuilding it, she actually is shown helping Cyborg with the biggest smile she's likely ever shown on the show.
To add to that, Raven can be seen in several subsequent episodes riding shotgun in the T-Car with Cyborg.
At the end of "Birthmark," the Titans throw a redo-birthday party for Raven:
Beast Boy:You may not like your birthday, but we're all glad you were born.
After having just gone through an episode-long brutal Mind Rape in "Haunted", Robin confesses to the other Titans that sometimes he feels like he's the only one still looking for Slade, "the only one that can stop him". Whereupon Starfire steps forward and tells him gently, "Robin... you are never alone."
Beast Boy and Raven's conversation at the end of 'The Beast Within'. Couples as a Crowning Moment of Funny: "We're having a moment. Don't ruin it."
Despite going through a bit of a psychotic episode, Beast Boy's only concern after turning into The Beast is to protect Raven from harm. When he transforms again near the end of the episode, he apparently cannot recognize the other Titans, yet still rushes to her side, apparently to protect her from what he thinks is a threat. This even carries over to part one of The End, which is the only other time he turns into The Beast (which is sort of implied to be his most powerful form). Once again, his only motivation is to protect Raven.
Doubling as a Tear Jerker: When Raven is lying unconscious in the infirmary, after being told that his DNA might be coming apart as a result of being doused by chemicals, Beast Boy still only cares about Raven, asking, "Raven...she's gonna be alright, isn't she? I mean...she's not moving. What have I done?"
Red X eliminating Robin's competition after the Boy Wonder saved his life can be viewed as heartwarming.
Somewhat understated, but Raven turning up with the kids from 'Hide and Seek' in tow in 'Titans Together'. Also, "fine, but stay away from anyone older than you". It really shows how attached she's become to them.
In "Forces of Nature", Beast Boy apologizes to Starfire for a prank when he is desperately trying to dig her out of a pile of rubble.
In "Mad Mod", Starfire fussing over a hypnotized Beast Boy.
At the very end of "Date With Destiny", after Kitten, Fang, and Killer Moth are arrested, Robin and Starfire are declared the king and queen of the prom. At which point, Robin says, "I guess one more dance wouldn't kill me" as he takes Starfire's hand and they go and dance together.
In "Switched", Starfire and Raven meditating together at the end.
All of "Hide and Seek", in which Raven eventually "adopts" three young super kids. Made even better by the fact that she starts out completely put off by them, but they eventually awaken a Mama Bear side to her. Notable moments include:
Teether giving Raven his pacifier as a parting gift.
Timmy putting his blankie over Raven when she was knocked unconscious briefly. A blanket that Raven repaired with a stapler, mind you.
"There is no Bobby. It’s you, Melvin. Your powers. You move things with your mind. You’re a big girl now. You’ve got to take charge of your powers and stop blaming things on your imaginary friend." - Raven says this in a way that you have to wonder if she's speaking from experience. In other words, she sees a bit of herself in Melvin.
Raven immediately realizing something feels and sounds very wrong, races back to the safe house, pounds on the doors while calling out the kids' names and busting the door down when she doesn't get a response.
Melvin: You can go home, Raven. Your friends need you.
Raven: What about you guys? I can't leave you kids all alone!
Melvin: We won't be, we've got Bobby and each other.
Raven: *while handing her own T-communicator to Melvin with a smile* And you've got me. Whenever you need me.
The kids grin excitedly, and jump forward to catch her in a group hug, with Raven actually accepting it with the same enthusiasm
Raven: *after a short while* ... Okay, that's enough now.
The kids return in the Grand Finale and wordlessly ask Raven if they can fight in the big battle. Raven's response?
Raven: Okay fine. But stay away from anyone older than you.
Beast Boy enthusiastically throwing his arms around Raven after Trigon's defeat.
A minor one, but it was really cute at how Starfire was really missing Robin in "The Quest"...despite the fact that he probably hadn't even been gone that long. Later, she gets a cute look of happiness on her face when she thinks Robin has returned...only to find Beast Boy in Robin's uniform. Finally, the way Starfire, as Robin, pretends to compliment the puppet of her.
In "Homecoming Part 2", when the Doom Patrol insist that Beast Boy has to go with them to complete a dangerous mission, the Titans rally to his defense. All of them - even Raven Raven loudly insists that he should be allowed to make up his own mind.
The team rallying around Starfire in "Troq" when they learn Val-Yor, the alien superhero they had befriended, is horribly racist against Tamaranians, and the alien word he calls her is actually a Fantastic Slur. Fittingly, it's Cyborg who first notices that she isn't getting along with Val-Yor and they discuss the nature of prejudice and racial slurs. The show doesn't directly mention the fact that he's African-American—instead he says he knows prejudice due to being half-robot—but the implication is obvious. And when they tell Robin about it, his reaction is priceless: no explosion, no yelling, just a cold, deadly "What?" The tone of his voice says he's about a second away from murdering the guy. At the end of the episode, the Titans clearly no longer idolize Val-Yor and tell him to kick rocks when he's unrepentant in his racism despite Starfire saving his life. She then explains to them that she values the words of her friends far more than she hopes some bigot changes his mind.
Just count how many times in the series Robin catches Starfire when she gets hit and falls out of the air. Squees may ensue.
Let's face it: this is Starfire's default state.
Mas y Menos reuniting during the finale.
"How Long is Forever" juxtaposes tearjerkers with heartwarming moments.
When Starfire gets flung into the future and meets Future-Cyborg, Cyborg can barely believe his eyes that she's really there. When he does accept it, he smiles. It's short but it conveys a lot of how happy he is just to see her again.
After failing to get help from her other three friends and getting her butt handed to her (along with a breaking speech that causes a Heroic BSOD) Starfire is saved by none other than Robin, or Nightwing as he goes by now. One thing of note, is that none of the other Future-Titans had had any contact with Robin for awhile, so he couldn't of heard about Starfire from them. But he found out on his own and made darn sure he was there to save her from Warp the second time around.
Nightwing in general as he brings Starfire back to his headquarters. One small but touching moment is when he puts a blanket around Starfire (for comfort) as she gazes forlornly at his old Robin costume. Also, when Starfire informs him that she now thinks that there is nothing they can do to fix the situation, saying it is impossible, he turns around and replies: "Good, because from what I recall, we've done the impossible before."
Also, Nightwing kept his Titan's communicator all those years so he could have some way of contacting his friends if the need came. Furthermore, all of the Future-Titans kept their own Communicators as well.
When Nightwing signals that he and Starfire need help, the rest of the Future-Titans come. Even with how crappy and bleak their life has gotten, they are still a family, and Starfire is the main glue that bound them together. Really highlights Starfire's status as The Heart of the team.
And of course, the scene towards the end of the movie where Robin admits to Starfire that they can be more than just teammates followed by their first real kiss was every shipper's dream come to life.
Can't forget this exchange at the end of the movie.
Cyborg: Guess you're not a wanted man anymore.
Robin: (Holding hands with Starfire) Oh, I wouldn't say that.
Really, the two are a goldmine for these. Check out the entire last half of Robin and Starfire's cave conversation in "Stranded", as well as when they hold hands and Robin says "As long as we're together, we'll be okay." Aww...
While Robin's actions in Masks are the reverse of heartwarming, the fact that he did it all because he was worried about Starfire certainly is.
After Raven's Heroic Sacrifice, when the remainder of the team realize she shared her powers with them, all of them reciting Raven's By the Power of Grayskull! line "Azarath Metrion Zinthos", serves as both a power-up phrase and a tribute to their friend.