In "Driver's Ed", the first thing Robin does after getting in a serious Batmobile wreck is to call Batman, who apparently offered to get down there right that minute to pick him up. It's kind of sweet how typically "father-son" that whole exchange is.
In "Dog Hand", when Raven is in a bad mood, while she doesn't answer when Beast Boy asks, and even lashes out in her demonic form when Cyborg pushes her on the matter; it is ultimately Robin that snaps her out of it and gets her to spill the beans on her Daddy Issues. It's even more heartwarming to the people that wrote the show because even though it was a semi-comedic approach to it, the writers knew of Raven's bond with Robin would stick in one episode at least.
Cyborg and Beast Boy making up after their pie fight.
Cyborg: Why were we ever fighting?
Beast Boy: I love pie.
Cyborg: I love you and pie.
Even though they pranked Beast Boy into thinking he was a ghost, the Titans were willing to stop him from jumping into a volcano. At the cost of their lives no less.
"Hey Pizza!" begins with Beast Boy and Silkie trying to stay cool. It's hard not to say "awww" when they bump fists while relaxing in an inflatable pool.
Robin sacrificing the pool, and a chance at seeing Starfire in an itsy-bitsy teeny-weeny yellow polkadot bikini, to build a senior center for the elderly.
Beast Boy and Starfire's relationship in "Starliar" is this for some viewers. Especially since this series tends to make all the Titans act like jerks. Here, they act much more like how they did in the original series.
The episode can best be described as adorable due to the fact they're both having genuine fun, up until Beast Boy realizes he's let things get out of hand, and even then it's still rather cute.
The ending comes off as a big sister playfully teasing a younger brother.
Starfire's lies cause Robin, Cyborg, and Raven to turn on each other. When it gets out of hand, Starfire comes clean and feels like leaving the Titans over what she's done. The Titans forgive her and each other and clean up the mess they made. Beast Boy even comments on how heartfelt that was.
It's pretty heartwarming that Raven can express her cracked tooth problem to her friends except Beast Boy. Her eyes when she nods at their questions show that she is genuinely frightened, but can't say why. It, of course, turns into a moment of funny when Beast Boy breaks her silence. Even Cyborg, who's the reason her tooth is cracked in the first place, didn't get it as rough.
In the same episode, Cyborg gives Beast Boy "tofu meatballs" since the latter is a vegetarian. Since the two often argued about meat vs. tofu in the original series, it's nice to see Cyborg respect Beast Boy's vegetarianism.
In "Terra-ized", Raven hinting at the end that she may have feelings for Beast Boy. Pretty heartwarming for both the Titans and their fans.
Also, a blink-and-you'll-miss-it moment, but Robin keeps a picture of Batman carrying him on his shoulders next to his bed. Awwwwww.
The reveal that Cyborg enjoys eating veggie burgers.
And that he started making them so he could share them with Beast Boy.
The end of the episode has Raven and Starfire staying by Dr. Light's side and waiting for help to arrive.
PEACE AND LOVE, PEACE AND LOVE.
Considering all the faults in Beast Boy that Raven pointed out in "Matched", comforting Beast Boy after revealing Terra's true nature and telling him he's fine just the way he is speaks volumes. Turns into something of a Tear Jerker near the end of the conversation:
Beast Boy: (heartbroken after seeing that Terra undeniably hates him) What's wrong with meeeee?!
Raven: There's nothing wrong with you...it's her, she's an awful person."
Beast Boy: No! There's a good side to her, Rave, I know it...I'm just not good enough for her.
Although it sucks for Raven, Beast Boy's love song to Terra and Terra actually falling for Beast Boy because of it, enough to stop attempting to kill him, counts too, as it shows his faith in her having a good side paid off.
Stafire giving Robin a kiss on the cheek (even though she says she views him like "the brother" afterwards).
The HIVE five becoming good and the Titans becoming evil so Cyborg and Jynx can be together.
The photo of Batman putting his hand on a younger Robin's head lovingly framed in the Batcave. (Batman's "thanks for cave-sitting" email even had "xoxo" at the end)
Silkie telling Starfire that he loves her in "Missing".
Silkie's dream with him dancing with Starfire.
The Titans comforting Cyborg on the loss of his grandma, or rather her voice.
Blackfire realizing her wrong doings and actually trying to make a bond with Starfire and the Titans. Unfortunately, Starfire changed so much in prison and she refused to accept her sister's apology. Though it looks like she does accept it after Blackfire gets beaten up.
The person Beast Boy considers to be the toughest: Raven. She reacts by blushing with a smile.
Likewise in "Sandwich Thief", when Robin was trying to find out who stole his "legendary sandwich", we see his method for interrogating each. Cyborg: took his head off, hooked it to a computer, and looked through his memories. Starfire: drugged, strapped into a lie detector, and asked questions. Beast Boy, teleported directly into his stomach by Raven. And for Raven, he asked her and she told him she didn't take it. Which means he trusts Raven's word more than Beast Boy, Cyborg, and even Starfire.
Starfire and Raven becoming each other's dad. It makes sense in context.
"The Mask": Robin refuses to take his mask off because he wants to protect the others.
"I know I don't say this often, but I really care about you guys."
Raven genuinely appreciating Robin's "uncle jokes" and complimenting on it, which has consistently remained a trait since it's debut episode.
A minor example, but in the episode about the campfire stories, Robin tells a rather sad story from a date he went on. Cyborg and Beast Boy make fun of him for it, calling him a "sad little man" (or something like that). When Robin looks sad about it, the bear (who was moments ago mauling him) hugs him and strokes his head to make him feel better. It's kind of nice to see Robin treated like that. But it also makes his teammates seem absolutely HORRIBLE in comparison, when a BEAR does more to make him feel better than they do.
Raven's story reveals that she largely appreciates that the team gave her a place to belong and that for all their differences, she doesn't have anything bad to say about Starfire.
Starfire cheering up Robin in the thanksgiving episode.
While subtle, when Beast Boy says that he brought a 'homeless family', Robin was more than willing to let them join up in their Thanksgiving meal.
In the episode "Salty Codgers," we get to see Robin and Starfire as elders slow dancing. We don't usually get to see Robin and Starfire having such sweet moments, so for Robin X Starfire fans, this is a very touching moment.
At first, "Scary Figure Dance" seems like a rehash of the hated "The Hive Five" episode, but the Titans were legitimately just having some fun with the Hive and they agreed at the end that it was actually kinda fun.
As much as "The True Meaning of Christmas" is full is Jerkassed moments, Santa giving the villains their presents at the end was admittedly kind of a sweet throw the dog a bone moment.
Beast Boy and Raven's first kiss in "Rocks and Water".
The beginning of "Hey You, Don't Forget About Me in Your Memory", where Beast Boy retells a story about the Titans' summer, with a heavy focus on Beast Boy and Raven's blossoming romance.
"How 'Bout Some Effort" Has Cyborg go on a quest to prove he really does like Jinx and prove he want to make up for earlier.
Starfire and Cyborg singing and frolicking in the garden in "Secret Garden".
Starfire giving up calling dibs on the TV remote to help Cybrog calm down and take him to her secret garden to relax.
Cyborg trying to get the rest of the team to stop calling dibs and calm down after calming himself.
He expresses guilt and regret over going against Starfire's wishes to keep the garden a secret from the rest of the team, despite having good intentions of trying to get Robin, Beast Boy and Raven to relax.
When Robin, Beast Boy, Raven and Starfire freak out and go on rampages in the city, Cyborg saves the day and calms them down by creating a new garden in the middle of the city.
The episode "Wally T.", which was done for a kid from the Make-a-Wish Foundation who really loves the show and wanted be in an episode as a character.
The whole episode was just heartwarming, since even though the show isn't loved by some, it acknowledges the fans it does have for basically giving the show its legs to stand on. What sells it is that Wally T. (WALLY T!!!!!!) looks so happy to be hanging out with the Titans.
The final shot of the episode is a thank you card for Wally T., signed by the real life cast and crew.
The conclusion for the girls in "Operation: Dude Rescue", especially Raven and Terra actually bonding when Raven admits that, aside from the whole revenge thing, she thinks Terra is cool and kind of likes her.