When Aeris died.
For me, no other scene from a videogame has evoked anywhere nearly as strong emotions.
I have tortured the knight of the realm and thrown him to the horned reaper when he turned to my side. I have beaten my minions to death just because I could. I have covered formerly peaceful lands with darkness.
I have knowingly and wilingly let a village starve, killed peasants, taken their daughters as slaves. I have mercilessly killed my opponents to further my own goals, I dumped my goody-two-shoes girlfriend for her sexier sister.
I have dropped nuclear bombs on cities, killing millions in one strike and obliterating the enemy's defenses in order to allow my troops to march in (I also cleaned up the pollution, climate change is BAD for the economy, it lowers food production). I have laid siege to my opponents while we were technically at peace by moving in diplomats first and then parking military units on the same spot, literally starving their cities to death.
I have battled my way through a research facility that was besieged by both aliens and the military, I have averted the end of humanity just to be kidnapped by a man in black with a suitcase.
I have had amnesia and fought for survival in a nuclear wasteland where the laws of nature no longer apply as they should, navigating the occasionally deadly politics and often deadly geography of a place I knew nothing about.
I have left my home and my friends to search for my father in a brave new world, I have saved a settlement from obliteration, eaten the corpses of those who had previously tried to kill me in order to survive, I have pondered the question of what measure a human is.
I have exposed and thwarted the plans of an evil organization bent on world domination with nothing but my wits, my camera, and a pirate broadcasting station. (The last game segment doesn't count!) I have seen the person who took care of me since I was born die in my arms and come back to life.
But only one game has ever truly moved me.
Other games may have been amusing, challenging, impressive, or even thought-provoking. But as for emotions, so far there's only one.