Basically what the title says. I've only played two games like this so far (Silent Hill 2 and OMORI) and am looking for more.
Could be games, ROM hacks, mods of existing games, etc.
EDIT: So many great suggestions! Getting a bit overwhelmed by how many there are, so I'm going to need to find a way to put this in some kind of list with an order to play the games in. By all means, keep 'em coming, though!
I was also going to say Brothers. There’s one moment (anyone who has played it probably knows what I’m talking about) that actually gave me a visceral reaction.
I've played through this game a few times over the years - twice playing with one of my kids. I've always played as the older brother, and every time it chokes me up at the end with the swimming part. My kids never seemed to mind, but it wrecks me.