*SPOILER ALERT*
Okay. There has been a lot of sad parts in the animes that I've watched already, but the one that is terribly, heart breaking sad has to be the scene from Angel Beats. I mean this show is full of fears and if that episode wasn't sad enough already they had to throw this in at the end.
After the others had "graduated" and moved on to the next world. Kanade and Otonashi go outside where he tells her that he wants Kanade to stay in the afterlife world with him. He says that he loves her to which she doesn't respond at first. It was then revealed that Kanade had received Otonashi's heart when she was still alive. She knows that she would disappear if he told her that he loved her again. He denies her request at first, but then he does.
She disappears shortly after thanking him leaving him empty armed and all alone and screaming out her name.
You'll just have to watch the episode because I can't do it enough justice. This part made me nearly cry and I never cry for anything animated or movie wise. The feels.... I can't deal with them even as I'm writing this now.
"Thank you for giving my life to me" - Kanade Tachibana
"My life after losing her... Is it over as well? The days I spent satisfied with the happiness I never noticed... Those times had passed away. For me... There's nothing left at all." - Yuzuru Otonashi