This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Haibane Renmei
Kuu's Day of Flight and Rakka's depression afterward.
The episode that showed Reki's past.
Rakka seeing the bird skeleton in the well and asking it for forgiveness.
At the end of the series, Reki begs Rakka to help her. On that note, Reki's despair in the final episode in general, as well as giving up on any hope she thought she had for salvation is quite sad to watch.
Admittedly, this troper cried more than he did in any story, including stories whose entire premise is founded on being a tearjerker, after Rakka pushed Reki out of the way of the Railroad Tracks of Doom. Although they were tears of relief as opposed to despair. I have yet to see another movie, series, or read a book or comic that made me break down as much.