Setsumi's tearful speech toward the end, in which she laments that she has no future and begs the protagonist to just let her give up. No fictional moment has ever brought me to Manly Tears quite like that.
Setsumi's suicide soon after. The music doesn't help.
Hell, ALL of the first game. You watch these two people drive around Japan, steal things, live out a Road Movie, and grow fond of each other. And then you realize, you've grown fond of them as well, but there's nothing you can do. Just... Goddamn...
In the prequel, Himeko and Setsumi taking their first and last road trip together. It gets worse as they slowly make their way up Mt. Fuji, with Setsumi feeling more and more helpless as time goes on, believing Himeko is going to commit suicide.
Himeko saying goodbye to Setsumi, knowing it's the last time she'll see her. "Farewell...Professor Croquette."
To cap it all off, the scene where the dying Yu relays the 'rules of the seventh floor' to Chihiro. The seventh floor itself is in the midst of reforming (Yu is the last of the old-system hospice patients), with promises of a better psychiatric care in the future. It makes a poignant moment of Passing the Torch, if short.