Rugrats/Heartwarming

• Tommy decided not to abandon Dil with the monkeys in the movie.

"My Tommy"
"My Dil"

• I can't recall the name of the episode, but it's the one where Angelica and her parents are moving. Angelica and the babies are all happy about it...except for Tommy, who says it's terrible and goes on to tell the story of how Angelica brought them together and it's because of her that they're friends. Angelica hears the whole story and is in tears afterwards and doesn't want to move. Probably heartwarming (IMO) because it shows Angelica's "heart of gold" side.
• Chas, Kira, Chuckie, and Kimi being a happy family.
  • Specifically, the first episode after the second movie, where Kira formally adopts Chuckie and Chas does the same with Kimi.
  • For this troper it's this one line in the second movie from Kira:

"Chuckie, how would you like to dance with your new mom?"

• The song sung between Tommy and Angelica during the All Growed Up TV special, as it shows clips of all the adventures they had as infants. Considering this was going to be the grande finale of the series, it was pretty poignant.
• Angelica saving the babies from Josh. "They may be just a buncha dumb babies, but they're my DUMB BABIES!"
• The Rugrats second Christmas special "Babies In Toyland": The babies find themselves in a Nativity scene and think the baby Jesus is real. They feel sorry for him since they believe Santa isn't coming and he's lying alone in a pile of hay with no gifts, so one by one, they each give him their own gift just because they want his Christmas to be special. When they found him, the figure's expression was neutral. When they're done, it's smiling. Awwww to the power of 10,000.
• "I'm a big brave dog." Whenever Chuckie comes out (inevitably nervously, and to himself) with this carefully-deployed catchphrase/mantra, a Heartwarming Moment generally won't be far away.
• The episode where the kids go to see the Dummi Bears on stage, but Angelica can't go due to a cold. The babies return, seeming to have caught Angelica's cold, but they were only faking because they wanted to be with her. Especially sweet when you remember how much Angelica bullies them. And everyone still got to see the show because Stu bought the video of it while they were there.
• The episode "Lady Luck." Grandpa goes to bingo night at a senior home, and due to his ramblings, the babies think he's going to meet a friend called "Lady Luck." They search all over the home looking for Lady Luck, in the process, turning the soporific home upside-down and helping all the elderly visitors to have a lot of fun. In the end, the previously-tough operator of the center, seeing how much fun the seniors are having, both becomes nicer and goes out with Grandpa for ice cream.
• The show's second Christmas Episode, particularly because it's not a Santamas episode. The babies actually encounter a Nativity scene and, despite not knowing who they're dealing with, give the half-naked baby in the manger some warm clothing. The baby doll and all the mannequins around them smile.
• The end of the Mother's Day episode with the poem Chuckie's mom wrote for him.

My Sweet Little Chuckie
Though I must leave you behind me,
this poem will tell you where you always can find me.
When a gentle wind blows, that's my hand on your face.
And when the tree gives you shade, that's my sheltering embrace.
When the sun gives you freckles, that's me tickling my boy.
When the rain wets your hair, those are my tears of joy.
When the long grass enfolds you, that's me holding you tight.
When the whippoorwill sings, that's me whispering, "Night night.".

• The episode where Susie's tricycle goes missing. She accuses Angelica of stealing it because Angelica had been mean to her earlier (which makes the assumption somewhat rational). As the episode goes on, it looks like Angelica did steal it and Susie ties her Cynthia doll to a balloon for Tommy to let go as revenge...only for it to be revealed later that Angelica didn't steal it after all. Someone else (I think Susie's mother) had moved the trike. After this, Angelica reveals she was making (well, trying to anyway) an apology card for Susie for being mean to her earlier. So we have an episode where Angelica, of all people, is apologetic. And to top it off, she does get her doll back.