This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Gunslinger Girl
Numerous portions of Gunslinger Girl, especially the backstories of the titular assassins, make almost any reader cry, cringe, or both. Triela's past in Snuff Film in particular raises the question of how much of a blessing the Conditioning is in a lot of these cases. Of course the mental disintegration of the kids is not easy to watch either — and neither is Angelica's eventual death after she protected her handler from a bomb attack. They really drive the point home by letting her tell that Fairy Tale to cheer up her handler, right before she dies. Doubly so as she doesn't even remember who he is, telling him the story that he told her.
Angelica's death in the first anime is just as much a Tear Jerker as the manga.
The whole blasted thing. Special mention goes to the Claes-focused episode in the first season.
And then there are the events in chapters 83 and 84. Holy schlamoly.
Triela's eventual discovery of how she and her handler came to the "Social Welfare Department", and how they choose to face her approaching mortality.
This scene from "A Day in the Life of Claes"
Claes: Have you ever been tremendously sad, but the tears won't come out? Jean: Sure...it happens. Claes: That's how I feel right now. My heart is overflowing with tears, but they just won't come out of my eyes. At night when I'm asleep, they quietly spill out onto the pillow without my noticing.
Especially at the end with a rendition of "Scarborough Fair". This one was done by Brina Palencia.
Henrietta fulfilling her earlier suicide pact with Giuse at his request. After getting fragged at her hands during a rampage, he has her finish the job and, as she does so, puts a bullet through her head.
The anime intro, using the Delgado's "Light Before We Land", is a painful, heart-wrenching summation of this entire series: yes, these children are trained killers, but they're still children. The first time you see the intro, don't be surprised if you miss the first few minutes of the episode following as you try to stop crying.
Henrietta being reconditioned is horrific. She's always been a happy, friendly kid and she's the protagonist. Suddenly all her memories are gone and her personality is reset to a complete blank.
Petra didn't die in the line of duty. She died from something as natural and inescapable as cancer. Even with all the advanced technology they couldn't cure her.
Or rather, they could have but the cost of doing so and extending her life until she'd die anyway due to her cyborgization was deemed too high. Not that that makes it any better.