In Bindinc of Isaac you cry a lot.
But on a more serious note. The Life is Strange series can be very emotional, if you like the style of the games.
A gaming community free from the hype and oversaturation of current releases, catering to gamers who wait at least 12 months after release to play a game. Whether it's price, waiting for bugs/issues to be patched, DLC to be released, don't meet the system requirements, or just haven't had the time to keep up with the latest releases.
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In Bindinc of Isaac you cry a lot.
But on a more serious note. The Life is Strange series can be very emotional, if you like the style of the games.
Cyberpunk 2077 and Horizon Zero Dawn are both fantastic games with an emotional storyline.
Detroit: Become Human had a really great character focused narrative where basically everyone can die. Give that one a go
The Last Day of June is quite lovely.
Portal 2. But you should play the first part before sequel, if you haven't already.
Telltale Games Walking Dead. Not a game, but a whole series.
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.
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)
You may already know it but Omori was heavily inspired by the mother series and especially Mother 3: https://twitter.com/_omocat/status/1384687971929006080
Death Stranding
That Dragon, Cancer. Part game, part visual novel.
Rime is hauntingly beautiful in a way that hits you as it finishes.
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.
Persona 4 Golden is a beautiful game that made me emotional more than once.
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.
One I've not seen mentioned but made me bawl my eyes out is 'Presentable Liberty' Im not sure about the remake, but the original was pretty short and was gripping, despite the low level of action.