Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
Tear Jerker: The Sarah Connor Chronicles
In the second season premiere, a rather berserk Cameron is trying to kill John, and John and Sarah have her pinned between two trucks. As John is trying to remove Cameron's processor chip, she begins asking him not to remove it, saying she's "fixed" herself. As John keeps working, she gets more desperate, and starts sobbing and begging more frantically, going so far as to shout she loves him. Even though you know that she's simply trying to escape, it doesn't change the emotion in her words.
All of "Allison from Palmdale." The juxtaposition between Allison's suffering in the future and Cameron's suffering as Allison in the present, especially the part where Cameron tries to call her "mother" who doesn't know who she is. Then, at the very end, we have Allison being choked to death by Cameron, while utterly refusing to help her assassinate John Connor. The scene in question is a borderline between a Tear Jerker and a Crowning Moment of Awesome for Allison for her defiance.
Especially the part where Allison talks about her birthday right before Judgment Day:
"July 22. I had a party in Griffith Park. My friends were there....I saw a boy ride by on a Solar mountain bike, and I told my dad, 'That's what I want.' And he said, 'Next year.' ....I didn't have a party next year. No one did. (...) ....everyone was dead."
In the episode "Self Made Man," Cameron makes a friend in the form of Eric, a wheelchair-bound research assistant at the history building at the university. Toward the end of the episode, Cameron's unwitting "weirdness" while pursuing the Terminator Stark has alienated Eric to the point where he finally demands that she leave. She does, and walks away, giving her only friend a look that is as close to confused pain and hurt as she possibly can get. Its hard to make a killer deathbot sympathetic.
Things get even better (or worse) in "Ourselves Alone". After finally making some headway healing her relationship with John, Cameron gives John her kill switch, in the shape of a locket made * just for him* . You'll just want to take that thing out and tell her she'll be all-ok. And don't cry.
Toward the end of "Today is the Day Part 1," the scene where John apologizes to Riley's dead body was absolutely heartbreaking. Alas, Poor Scrappy, indeed.
A subtle but very upsetting moment comes at the end of "Automatic for the People", where Sarah keeps pressing Cameron for answers about whether she'll get cancer, culminating in Sarah getting frustrated and asking "What do I do, just wait? Like a time bomb, am I just going to go off some day?" Cameron quietly replies: "I don't know...am I?" This is made so much worse by knowing that while Sarah, John and Derek will all do their best to help each other, no one is going to comfort Cameron; she's just a machine, after all. She's scared, of herself, and she's alone. Just thinking about that makes me cry.
In the penultimate episode, John is talking to Savannah Weaver, whom they just rescued from another terminator. She remembers him from one of their brief encounters before, at the psychiatrist's office. Savannah says that he's dead, and he was her friend, and she misses him... Which is sad enough, coming from a child, but then asks if Derek was a friend of John's, and then blames herself for his death. If the parallels between John and Savannah weren't obvious already, it becomes painfully so right at that moment.
In the series finale, when they reach the basement only to discover that Cameron has given her chip to John Henry, who just time-traveled to the future. One of the screens displays the words: "I'M SORRY JOHN" being repeated over and over and over again. John has already lost one protector terminator, which served as a protective father/uncle figure to him. And now he's lost another protector, who in this case is somewhere between a sibling and a lover. He's going to be so desperate to go after her.
At the end of Adam Raised a Cain, when Sarah is arrested.