This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Ghost in the Shell: Stand Alone Complex
The manga adaptation of "Testation" is one, especially after the Major jacks into Kago's cyberbrain.
The track "Beauty is Within Us" also hammers Kago's intention with the episode.
While much of "Time of the Machines" is played for laughs. Kusanagi's reservations regarding the Tachikomas and eventual decision to have them dismantled is not. Not to mention the poor Tachikomas lack of understanding about her concerns. The poor things think that she's mad at them and attempt to avoid punishment by hatching a bizarre scheme to appeal to her and prevent their removal. And when they (understandably) spy on her and Batou's conference, they are lead to believe that she was actually angry at him and not them. So they decide to throw him a party to make him feel better, they all get shipped back to the lab a few days later...
Most of "A Tachikoma Runs Away".
In the climax of the first season, when the Tachikomas sacrifice themselves to save Batou, using the very few weapons they have. His personal Tachikoma is the last to go, and it looks to Batou, says, "Goodbye, Mr. Batou..." and cries a single tear of organic oil. That was especially heartbreaking because of the symbolism of humanity that Batou literally installed by giving the Tachikomas organic oil to begin with. They get better, but the fact that robotic armaments being scrapped can cause real world tears... Wow.
Batou's horror as he realizes exactly what they're doing.
"What you have is certainly not weak."
That oil tear also calls back to In an earlier episode, when a Tachikoma ran away and said it couldn't cry in the same way as a little girl, Miki, that it had befriended. It still cried an oil tear to match up with the girl, possibly so she wouldn't feel alone. The fact that this time the Tachikoma cried only because of it's own situation suggested it might have attained a new level of sapience, that it truly had gained Ghost after all.
The third episode of the first season, "Android and I", especially the end when he realized that the android, Jeri, admitted to being in love with the Canadian ambassador's son who was willing to die to keep them from being captured. When Togusa watches the movie "Breathless" at the end and asks his wife where the extra lines are at the end of the movie, she replied that there were none (because the Jeri repeated the lines verbatim before they were caught).
In the sixteenth episode of the first season, "Ag 2 O," the Tachikomas just got shipped off, leaving Batou in a subtle bit of turmoil before he has to investigate a former boxing champion that was a personal hero of his. By the end of the episode the man's been arrested for leaking military info, and Batou, in sheer frustration at the man throwing away everything for more profit when he already had a loving wife and comfortable life as is, practically smashes the liquor the man's wife had given him and furiously throws himself back into training while cursing the man.
The end of 2nd Gig's "Trans_Parent." The VO who provided the little girl's voice earned her pay. When you watch the little girl struggle to get out of her wheelchair and try to find her father only to discover that she's blind AND crippled it's hard to fight the tears when you know that she will never hear his voice or receive a gift from him again.
"I don't believe it. Do you want to know something? I'd bet anything that all of you have ghosts."
While not actually sung by the Tachikomas, their theme song "be human" is both hilarious ("If I just could be more human, I'd have so many little babies and maybe a wife") and gutwrenching, underscoring the contrast between the Tachikomas who want to be human because they see their existence of specialized function as a curse, to the humans who want to be more like robots so they can perform better. One comment left on a youtube upload of the song:
I am not an emotional man. I am not bothered by horrific crimes or tragedy. While I believe human life has value, I do not grieve at its loss. I am not moved by random acts of kindness. God help me, this song made me cry.
From the moment I Do starts to the big boom, I could feel my throat tighten.
Most of the flashback portion of episode 11 of 2nd GIG (AFFECTION), but especially the one line toward the end:
"I'm going to practice folding paper cranes so that I can make them for you someday, okay?"
It got me at "She is probably still looking for the first boy she ever loved" I was watching the sub, so I read the text and was instantly in tears before Motoko's VA even stopped speaking.
What does it for this troper is the part where she ends making a mistake and tearing the paper crane she was making. You can clearly see how much effort she's putting in it, the sound of that tear might as well be the sound of her young heart breaking.
Cue the song Take a Little Hand, and this troper consequently bursting into tears.
After taking Dr. Asura into custody for trying to defect to North America, Batou's Tachikoma is sad because it didn't want his memories deleted on orders from the Major. Batou also asked the Major if the Tachikomas could visit him in case he's placed under house arrest.
The end of the episode "Excavation" is definitely a gut-wrencher.
The state of New Tokyo looks so incredibly sorry. Whatever that happened during the war must be really bad...
Togusa started as a Wide-Eyed Idealist, but by Solid State Society, he's become a lot more ruthless and cynical. However sad that is, it does not compare to later in Solid State Society, when he is prepared to shoot himself in the head to stop the Puppeteer from taking his daughter; showing Togusa is still a family man with ideals and ready to even die for his family.
Using his Mateba to do so, no less. The gun he clung to for the entire series, and supposedly got rid of by the time of Solid State Society.
Episode 7 of 2nd Gig has Section 9 helping a group of soldiers transport plutonium through an impoverished city. Some desperate refugees show up looking to rob the convoy, and Godha comments to the a panicking soldier that a refugee is carrying a pistol. This starts a shoot out which kills most of the refugees. We see afterwords that the refugee was just carrying a bent pipe, and the entire shoot out could have likely been avoided.