Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
Tear Jerker: Kaiba
Kaiba has a few examples of this, but there's one that stands above the rest. Chroniko, a cheerful and optimistic girl, decides to sell her body in order to feed her family (literally, because memories can be transfered). She's killed when a Bastard scientist releases her memories after extracting them from her body. Her surrogate mother, her aunt, couldn't care less, since she considers it one less mouth to feed, and that she's taken care of her sister's kid long enough. However when her aunt restored her memories, the truth finally came out. She loves Chroniko, too much until she had to remove her memories of her loving Chronico so she can let her sell her body. Cue sad piano theme, tears, and name screaming.
That's one of the prime TearJerkers of the show, but it's far from the only one. The very next episode has Kaiba trying to go inside an old woman's mind to find the treasure her and her late husband hid. The problem is that she keeps speaking as if her husband is still alive. Finally, three different version of the woman appear and begin to chide her for denying his death, taunting her over and over again until she bursts into tears.
The woman's husband appears in her mind. They begin to talk (the two shifting ages between camera cuts), and the old man reveals that he died trying to pick a rare flower for her on the top of their windmill. In the end the woman crosses over to the "black" half of her mind and embraces her husband, and dies. Kaiba and Vanilla bury her, and the viewer sees the same flowers sprouting from her grave.