This is based on opinion. Please don't list it on a work's trope example list.
Tearjerker / Star Trek: The Animated Series
Subverted in "Yesteryear" in that when Spock decides that his mortally wounded pet sehlat had to be put down, that is the moment when he embraces the Vulcan way of emotional control and logic.
Played straight in that it's a heartbreaking moment for Amanda; and also to Adult Spock, when he comforts his dying pet.
Also from "Yesteryear", the glimpses at Spock's childhood. The poor guy has been getting mocked and humiliated since long before what the original series shows. It gets even worse because Sarek, rather than being annoyed at the Vulcan children for (illogically and emotionally) picking on his son, gets disappointed at Spock for not being more Vulcan. Oh, Spock, you Stoic Woobie, you...
In "Beyond the Farthest Star" the villain is an energy being that has been alone for 300 million years. After it is defeated, its despairing pleas not to be left behind once more are surprisingly heartrending.