There's so many games that have moved me incredibly.
Source games (Mainly TF2, NMRIH, and L4D2) - No more room in hell was practically my childhood and the GOAT zombie game. Everything from it's dreary atmosphere to it's atmospheric and often haunting soundtrack was killer. Also,
the fukkery was so ripe as a youngin. Since it was a small game, and everyone knew each other (it wasn't too uncommon to even catch Devs), fukkery was a daily. The amount of fukkery you encounter on old source games is crazy, you could choose any and so long as you visit a server at the same time each day, you'll run into the same people/groups over and over again and start to piece things together. Don't like that group? Choose another server and pick a time. Source games are honestly too racist to play now. You'll hear and see some insane things these days, so beware
Silent hill (mainly born from a wish) - M favorite game series of all time. I played the first 4 games out of order and well after they came out, but born from a wish was special. While not a full game, the psychological story telling was really good and was a high point to me. It left me wondering what Maria actually was for months.
Doki Doki literature club
Perceptions of the dead
FNAF - The first one was really good when it came out, I have no idea what it's about now though.
Undertale