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!
There are a million things that you can do in the game, but you don’t have to do any of them. You can stick to the story if you want. It’s probably still a very long game though, even if you only engage in the story.