None. Most games I play, even with amazing stories do not impact me in any way except for that feeling of awesomeness for a few days. Or maybe I'm not playing enough games.
Or maybe you are an old man who cares not for actually good video games and only loves the retro crap without stories?
Persona 3 for sure though. Since I did beat it 3 days before my father died and the entire damn game is all about death... I do think that game did help massively with my own grieving processes. There is a damn good reason why I am now buying each atlus game to come out now. They have earned my money.
Fragile Dreams: Farewell Ruins of the Moon.
It is Grave of the Fireflies the video game... that should be enough to state that this is the saddest video game ever made... ever. Depressed people should never play it because it may actually kill them by making them kill themselves... I mean that in the most non joking way possible.
People need to realize that games are art. Seriously, it's been proven over and over again. I think it's about time to people to man up and finally say this.