Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
Tear Jerker: Lexx
The final act of the series finale is, though ultimately better than a Bittersweet Ending, absolutely heartbreaking.
Lexx may be a 6000 year old Manhattan sized insect who enjoys blowing up planets, but in the series finale as Lexx is dying of old age, his voice slowing down as it becomes harder to speak, he tells Stan that he "was always my favourite captain" and that he's going t miss him. You can't help but feel sad for the big bug.
Also from the finale:
Lexx: You are my favorite captain. And Stan?
Stan:[Annoyed and impatient] Yes, Lexx?
Lexx: I'm going to...miss...you...
Stan: I'm going... [Mood visibly shifts] ...I'm going to miss you too, Lexx...
Zev's death in "Terminal".
Zev: I had a good life with you guys. I did all right for a girl who grew up in a box.
Zev's speech in "Eating Pattern", after burying Kai (they believe him to be dead for good at this point), as she struggles to keep from crying:
Zev: Last of the Brunnen-G: if you were alive... (stops, holds back tears, starts again) Last of the Brunnen-G: if you were alive, I'd want you to be the first man... I... I used to want to die. But now, I want to live. I think that's because after meeting you, I realised that people aren't always that bad.
This moment from "Giga Shadow", which also serves as a reminder that Zev has a lack of general knowledge due to her lonely upbringing:
Zev: I'm making eye water again - it happens when I feel this way.
Zev's reaction to Kai's "death" in "Giga Shadow" is heart-rending.
Stan's obvious guilt and regret at his past actions during "Stan's Trial" can get this reaction.