Have you played Plague Tale 1 and 2? I'm not considered a very emotional person, but the dynamic really got to me. Just a really solid game, enjoyable combat. They're two of the very few games I binged to completion.
Patient Gamers
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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Portal 2. But you should play the first part before sequel, if you haven't already.
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.
That Dragon, Cancer. Part game, part visual novel.
Death Stranding
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.
Telltale Games Walking Dead. Not a game, but a whole series.
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
Rime is hauntingly beautiful in a way that hits you as it finishes.
Plague Tale (Both games are solid, but 2 was sooooo good)
The most recent one to make me cry was...
"I Was a Teenage Exocolonist"
People already recommended some Final Fantasies, but really all of them can get you quite emotional at times.
If you like VNs, Umineko no Naku Koro ni made me cry so many times...
Edit: Just remembered Once on a Windswept Night, it's just a short game you can complete in a hour, but for some reason it made me really emotional.