The Last Day of June is quite lovely.

Cyberpunk 2077 and Horizon Zero Dawn are both fantastic games with an emotional storyline.

Don't think I've seen anyone mention Oneshot. Amazing little game.

Plague Tale (Both games are solid, but 2 was sooooo good)

That Dragon, Cancer. Part game, part visual novel.

Papers, Please. Maybe not crying, but could definitely put you into a depressed mood if you manage to get into character. Needing to make a choice between letting some poor bastard's wife follow him without proper papers and feeding your family is tough.

Death Stranding

Persona 4 Golden is a beautiful game that made me emotional more than once.

Titanfall 2... Goodness that ending had my kiddo misty eyed. As for me, there was dust in my hand room or my allergies were acting up.

Had a quick scroll through and didn't see it anywhere yet, so:

Dear Esther.

Actually, reminds me I should play through it again, it's been a few years.

Rime is hauntingly beautiful in a way that hits you as it finishes.

Haven't actually played it yet but a video about MOTHER 3 made me cry just talking about the story (not only that but the part where he talked about the story made me a little emotional)

Here is the video btw

You may already know it but Omori was heavily inspired by the mother series and especially Mother 3: https://twitter.com/_omocat/status/1384687971929006080

Mother 3 got me tearing up when I first played it

Telltale Games Walking Dead. Not a game, but a whole series.

Tales, Xenogears

Portal 2. But you should play the first part before sequel, if you haven't already.