A very minor one in Chapter 1. Littlepip reads the override code which will open Stable 2's door, left by Sweetie Belle which is "CMC3BFF" - clearly short for "Cutie Mark Crusaders Three Best Friends Forever".
The end of chapter 17 and opening of chapter 18. After lusting after Velvet Remedy for so long, with little to show for it, LittlePip finds that Homage, the Tenpony Tower unicorn is interested in her. The date they go on is very awww-inducing.
Chapter 18, Littlepip is feeling messed up knowing she can't bail out Monterey Jack lest she sacrifice the romantic relationship she has with Homage, and tells her companions that she's going for a walk. All of her current companions (Steelhooves, Velvet and Calamity) insist on following her. It may be that they expect her to run into trouble given her predisposition for being curious, but the fact that they'll follow her hoofprints into any danger (or even just a walk) with her, even when she doesn't ask them to, is sweet.
Chapter 22 Littlepip promising an adventure with just her and Calamity after the latter starts feeling left out.
The opening of Chapters 25 and 27 follow Littlepip's thoughts on her companions in respect of friendship and family. Particularly effective in the former as this line of thought leads to her feeling lonely and weak without her friends only to receive a welcomed visit from Pyrelight.
Chapter 28, when Steel Hooves goes on the announcement in Stable 2, declaring to all the true oath of a Steel Ranger.
After Canterlot. When Littlepip is tired, worn out, sick, and at her weakest, the Black Book tries to prey on her, tempt her into using it. Convince her it is the only way for her to survive, to fight. And she nearly gives in, until, the spirits of the Mane 6 step in to help aid her. Countering all the Black Books taunts at Li'lpip. Helping her see her own virtues, giving her the strength to keep fighting. And at the end, showing her how wrong she was about herself. Helping her see just what her soul truly looked like. Not simply a battered, bleeding, dying raider. But a pony willing to sacrifice herself, simply to warn total strangers of a threat. Give them time to save themselves.
That entire chapter was pretty heartwarming. It includes a Thank-You party for Ditzy Doo for saving them from the Enclave.
After killing the Goddess, Littlepip sees that one alicorn has turned purple, with Twilight's cutie mark. Littlepip manages to take the message that Pinkie Pie left before the megaspells hit and play it for her, so that if Twilight is even still alive, she'll know that Pinkie acknowledged she had a problem and really wanted her there with her. Hopefully it got through...
"For the longest time, I had thought of myself as Red Eye’s reflection (granting one of Pinkie Pie’s particularly warped funhouse mirrors). But I was comparing myself to the wrong pony. I wasn’t Red Eye. I was Applesnack."
One moment in the logs of that unicorn scholar that lives in Zebratown. Pinkie Pie and some members of the Ministry of Morale come to Zebratown and at one point hide outside the house of one family. You think they're going to get jumped and arrested...then it turns out that its the birthday of the family's little daughter and the Ministry of Morale throws her a party.
The party is set to leave for Canterlot, and Homage asks Littlepip "promise you'll see me again." Littlepip makes a Pinkie Pie Promise that she will. Things start falling apart, and the Enclave attacks, cutting off Homage's broadcasts, prompting her to leave Tenpony Tower to go on a personal mission to wipe out one of the S.P.P. towers to distract the Enclave and regain control of her ability to broadcast, and is on the run for the remainder of the story. As it becomes more apparent that Littlepip will have to sacrifice herself to take control of the Single Pony Project, it seems like Littlepip will have to also break her promise to see Homage again. Then she meets Celestia, imprisoned in a Crusader Mainframe, and she is given the opportunity to look over her friends- including Homage. And even though Homage can't see or hear her, she senses Littlepip watching from a camera possibly hundreds of miles away which she should not even be able to see; and mouths the words "I love you, Littlepip." In the end, Littlepip is able to keep her Pinkie Pie Promise and generate a humungous tearjerker and heartwarmer in the best possible way.
“I’m here. And I’m not leaving you.”
The Afterword, which is just a much as a Tear Jerker too. We discover that Fluttershy was able to recover from the effects of killing joke. But we also see how much it still torments her. We also see happy endings for Ditzy Doo and other characters as well as an optimistic ending.
We even get some implied relief to a major Tear Jerker: Littlepip had trapped herself in the Single Pegasus Project, essentially putting herself into an And I Must Scream state like Princess Celestia, but with more control over the weather. However, in the Afterword, it's mentioned that Homage is visiting Littlepip due to it being the former's birthday. One could interpret that as meaning that Littlepip can actually leave the pod to see her friends if they come to visit; she just has to be in the pod to keep the weather under control. At the very least, it means she and Homage can still see each other (and have sexy times).