This series has quite a few Tear Jerker moments, considering everyone's already dead and they all had shit pasts when they were alive, but the disappearances of BOTH main vocalists of Girls Dead Monster in episodes 3 and 10 get special mention out of a million. Episode 10 especially because it gets you out of nowhere with Hinata accepting Yui's proposal, the explanation of how he'll marry her, the visuals of the would-be love story and Yui's disappearance, all too beautiful-but-tearjerking song by Yui.
Episode 10. With an emotional song to go along with it, after Hinata proposes to Yui there is a montage of their imagined life falling in love. It ends with a shot of Yui's baseball helmet and bat. On the ground. Yui is gone.
The ending of episode 6 definitely qualifies.
Otonashi: Your life was real too!
Also, the end of episode 12. Yurippe resists accepting her past and disappearing, but then we get this little gem from her siblings. It does NOT help that the depressing ending theme plays over this exchange.
Yurippe's siblings: It's okay. You've done enough. You don't have to suffer by yourself anymore. Thank you for thinking about us for so long, Onee-san!
Unless you're a Yuri hater, her origin story in the second episode. It's especially bad if you have younger siblings.
Otonashi's origin story also qualifies.
Especially the part that is told in Episode 9.
The end of episode 10 with that could-have-been love story between Hinata and Yui, especially with that sad song playing in the background. Damn you, Maeda!
The end of episode 12 when Yuri breaks down in to tears while the ending theme plays in the background.
In episode 13, when Naoi says he was leaving first and took off his hat revealing his teary face.
The very end, Yuzuru confesses his love to Kanade. She sadly had to tell Otonashi to confess his feelings again so that she'd disappear. He eventually does it, and she disappears. He breaks down into tears.
The final episode is by far the worst. The graduation scene was sad enough, with everyone leaving and quite likely never going to see each other again. But then, Kanade and Otonashi stay behind and go outside, where Otonashi confesses that he loves Kanade, and asks her to stay with him to help whoever enters the world after all of them. Unfortunately for everyone, she declines (though she does reciprocate the feeling), and reveals that her last regret is not being able to thank the donor of the heart transplant she received - and that donor happens to be Otonashi. They embrace, and there is an ensuing combination of Kanade thanking Otonashi over and over again and Otonashi screaming "KANADE! PLEASE DON'T DISAPPEAR! KANADE——!". The accompanying music doesn't help in the slightest. (The after-the-credits scene of them meeting in a next life helps a bit (depending on your definition of "help" - it might make you cry more); but it's almost like the producers were watching the final product and realised that that was just too much, and threw together something at the last minute to mitigate the pain.)
The worst punch comes right after she disappears and Otonashi spends a few seconds desperately clawing at the air where she just was.
The other epilogue has Otonashi actually stay behind in "Purgatory" to help other souls move on. Alone. Even worse, it seems that he's waiting for someone...
The scene where he sits alone in the council room was especially moving, especially if you see the pictures pinned on the board.
Hopefully you're reassured, Episode 9, Angel confirmed that when you move on, you go to a higher plane of existence.
Then again, who says it's the truth?
Keep in mind, Kanade has no more inside knowledge than anyone else in the series. She's just been there a while and come to her conclusions based on observation. But she doesn't know any more than we do.
If we are to believe The Stinger, then we can (hopefully...) assume she's right.
Not even the voice actors were immune to the sadness of this series. Emily Neves-Love, the voice actress of Angel, was crying her eyes out while she was recording the very dialogue she was speaking.
The Credits of the last episode. If you have somehow kept a dry eye through all of Episode 13, this will be the final nail in your coffin. In most of the credits sequences we see the SSS members appear on screen, one by one. In the finale, the credits start with everyone already there, including, for the first time, Angel. But this time, they fade. It goes down the line and ends with Naoi, then Hinata, then Yuri...and then, just about the time the viewer realizes that Otonashi and Angel are smiling at each other...Angel fades...and finally, Otonashi. Bravo, Key.
The scene when Otonashi fills out his organ donor card. The way he still keeps going, even though he's pretty much already gone.