This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / RainbowDoubleDash's Lunaverse
After the main conflict of Boast Busted ends, Trixie gets a chance to talk to Twilight one on one. After pointing out that she could have her arrested for her actions, she instead attempts to establish a connection by admitting her own mistakes and flaws, and reaching out to Twilight. Not only is this rejected, it only fuels Twilight's conviction that it's not her fault. In other words, Trixie trying to be a good pony gets twisted into 'evidence' that she's anything but.
Trixie later writes to Luna and shamefully admits how far she has yet to go when it comes to learning how to be a good friend.
The fifth chapter, added after the Lunaverse had been well established, gives us Shining Armor's reaction when Princess Luna informs him of recent events.
Trixie's story of how she got her cutie mark in Longest Night, Longest Day. Doubles as a Heartwarming Moment revealing more of her caring side, but still.
Chapter 5 of Family Matters, which is appropriately titled Catharsis.
The entire situation is just heartwrenching. Dinky and Amethyst Star are just innocent victims, and seeing Sparkler lash out and punish a foal for being in the same situation as her...
Elements of Insanity starts with Twilight putting her own spin on Pinkie's Brew, with Shining Armor providing unknowing accompaniment.
The song further ends with Twilight lamenting that all she really wants is to just be able to go home, but unable to bring herself to return to her family in shame without clearing her name first.
Tales of Ponyville gives us a doubly awkward moment where, after a prolonged misunderstanding, Raindropsbreaks down in tears believing that Trixie is constantly scared of her anger issues. Trixie actually panicked due to blaming herself of the misunderstanding, afraid that it might potentially ruin their friendship.
The revelation that Trixie kept a list of all the friends she's ever had, and how she's not friends with any of them anymore. She doesn't have canon Twilight's problem of not knowing how to make friends, she has the rather more depressing problem of that she doesn't know how to keep them. She's utterly mortified that Raindrops will leave her, and she'll be without friends again soon enough.
An Early Reunion. In Chapter 7, "The Alicorn Proof", after Cadence has worked so hard to prove herself to Luna, she discovers that it's impossible for her to be Celestia, completely shattering her self-perception.
What makes this worse is Luna revealing that every time she raises the sun, she feels her imprisoned, insane sister's anger and rage and hatred.
Chapter 8 follows this up with the "Revelation" of how Luna brought down her sister: she split off a part of herself which became Nightmare Moon as part of a gambit to not only distract and defeat her sister, but to destroy her own darkness. That darkness? Was purified by the Elements of Harmony and was reborn. As Cadenza.
Piano Amour's performance of the Sympony for Moon and Sun on many levels. Every musician who had attempted to recreate the missing fifth movement failed to meet Princess Luna's standards and ended with the musician blackballed for the rest of their lives. At the time of Piano's attempt, the once wealthy and respected Amour family were on the brink of destitution, and attempts to contact the Princess for assistance had failed. Hovering right on the edge of the Despair Event Horizon, Piano takes on the symphony that has ruined the careers of so many musicians before her, figuring that it doesn't matter what the Princess does to her as long as it gives Piano a chance to talk to her. In the end, she succeeds in drawing Luna's attention to the plight of her family, but while the Princess agrees to help them, she is still so furious at Piano's interpretation of the fifth movement that she is never able to play in public again.
Trixie's Heroic B.S.O.D. in "At the Grand Galloping Gala", when she realizes that her true political enemy isn't any specific pony in the Night Court, but the institution of the Night Court itself. After wanting to take part in it for so long, only to suddenly see the Court itself as a source of corruption, it completely breaks her spirit.
In the following chapter, learning that Princess Luna has basically given up on ever permanently fixing the Night Court is pretty depressing in its own right. Over the last thousand years, she's come to accept that there will always be corruption and greed among its members, and the best she can do is prune where she can, letting all the corruption she can't detect or prove pile up until an eventual purging. Trixie attempts to call her out on this, complaining about how unfair it is that they have to play by the rules when the corrupt Night Court members obviously won't.
Luna also specifically laments the thought that Night Light has just proven himself too corrupt to retain, as she had hoped he was one of the better ones. But he's allowed his grief and inability to protect his daughter from herself to blind him, turning him into somepony capable of letting an entire town suffer just to hurt Trixie.
Later, she has a private breakdown at the end of the appropriately titled chapter The Castigation of the Night Court, after her interrogation of Zizanie revealed that there isn't a single member of it who is completely clean of corruption.
Countdown To Crisis begins with Shining Armor and the Shadowbolts catching up to Twilight in Latigo. After catching her in a barrier, Shining begs his sister to come home, expressing his worry over their father's emotional state caused by her disappearance and fugitive status. Unfortunately, backing Twilight into a corner only causes her to have an emotional breakdown and escape by using a very powerful and dangerous spell that actually fractures reality when she casts it.
The chapter of Eye of the Hurricane where it's revealed that the treatment Raindrops received to deal with her constant anger issues has side effects. Lyra finds Pinkie Pie broken down in tears after Raindrops said viciously hurtful things about her, but the real kicker is when she visits Ponyville Elementary and, in front of everypony, says absolutely horrible things about her little brother Snails. As if that weren't enough, there's a heavy dose of creepiness when Cheerilee, driven into a Mama Bear rage, is about to beat Raindrops into the ground, only to stop when she sees her friend with a frozen smile and tears streaming down her face. The details make it even worse.
Lunaverse!Luna and Maneverse!Celestia wing-hugging in Crisis On Two Equestrias... which is defnitely a Heartwarming Moment, but the dialogue here seals it as one.
Celestia looked uncomfortable as she managed to get herself into a sitting position. “Princess Luna,” she said. “I am not your sister.”
“I know…” Luna breathed, not moving. “I know, but please, just for a moment…let me pretend…”
Dinky's Birthday, which is about... Dinky's birthday, but more specifically how Ditzy is watching her little filly grow up and her fear of being left behind and forgotten by the one pony that means more to her than her life itself. The Adult Fear elements and scenarios that Ditzy conjures up are heartbreaking.
The end of "Chasing Smoke". For all that she's been a childish jackass, Yangin has been dragged into a fight she wanted no part of, and gets screwed over by her own sister and handed over to Kindle, who as a djin she's forced to obey.
Then there's Dunya, who soars over the Moral Event Horizon for doing what she does out of spite, but she does have a reason to be cross, having been left on her own for over a thousand years, while her sister went out into the world, and as far as Dunya knows never even bothered looking for her. What she does is inexcusable, but it's hard not to feel some sympathy for what happened to her beforehand.