Trying to think of something in which the game conjures up emotions and not something through nostalgia.
Definitely Shadow of the Colossus. I played that on the PS2 years after the fact and yea, just a really moving game, it's awesome.
Panzer Dragoon Saga, mostly due to the music. Holy smokes it is good. Just listen to that shit, God-Tier. It really is an absolute masterclass in pacing and game design. I don't think it's the GOAT but it's definitely up there. It really is pretty much as good as people make it out to be. Just a solid experience through and through.
Also, FF7: Crisis Core. I honestly never really cared for Aeris, I played CC prior to Remake releasing, she's handled so well in that game. I love the way they portrayed her and the relationship between her and Zack, sad game.
FF7: Remake: Biggs, Wedge, Jesse. I haven't even finished the game but man, I effing love those characters and everytime they were on screen they absolutely stole the show. It was a bummer playing the game and knowing what happens to them. I really need to get back to that, I loved what I played of it at launch.
Dragon Quest 5: Just such an epic journey and again, the OST really drives the feels. The story/script is top notch too.