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!
Spiritfarer. I loved it on switch, but it's also on steam.
"Spiritfarer® is a cozy management game about dying. As ferrymaster to the deceased, build a boat to explore the world, care for your spirit friends, and release them into the afterlife."
For some shorter experiences I haven't seen mentioned when skimming through a few comments here, I definitely recommend trying Transistor. It was one of the strongest emotional experience I've ever had in a game. I've managed to play it in a single sitting, but it is around 6 hours long. Supergiant games make such a uniquely perfect audiovisual experiences, that every game from them is a treat, but Transistor is the strongest emotional experience I've played from them.
Another one would be two-hours long walking simulator with amazing environmental storytelling - What Remains of Edit Finch. You can play it in a single sitting, and it's gorgeous and really well done.
You should also play Hellblade: Senua's Sacrifice . It's also around 8 hours long, and you definitely want to play it with headphones, it's such a strong emotional experience. The audio and game design is so well done, and the game has stuck with me for such a long time. It's one of the few games where just seeing the trailer again tears me up and gives me chills. And after you play it, I recommend watching the documentary about how they tried to protray the mental illness of the main character through game design - it's such masterfully done that I didn't even realize most of what they are doing, but it has stuck with me and it worked wonders to make the experience even better.
And for some even more unique game design - Before Your Eyes. What makes this experience so strong is the whole premise of looking over your life and memories after you've died, with the main mechanic of how to advance time being by blinking - physically blinking, because the game can work with your camera. That makes for a pretty strong metaphor that makes it even more emotional experience.
And just to mention some games others have mentioned, to add to their recommendations - Outer Wilds, Ori and the Blind Forest, Life is Strange, Planet of Lana, all are really good games!
Chrono Trigger. A timeless game that will make you laugh and cry and experience all that in between. The sequel Chrono Cross is also great but the original is just unrivalled.
I was going through a really rough time when I played both of those games. There was something in Before the Storm that I know was coming but I cried anyways, multiple times. I’ve never been that invested in a game before and I don’t know if I’ll ever be again.
I cried at the ending of Outer Wields. Its was very beautiful. You need to search the story for yourself and complete little puzzle. At the end when you get the full story its just beautiful and scary.
I'd have to say Nier Automata, as well as the recent remaster of the game that came before it, Nier Replicant (ver 1.22...). Both are soul-crushing, which is helped by their amazing soundtracks. I definitely recommend them if you're looking for something to make you cry.
Brothers: a tale of two sons. You play as both brothers, working together to find a cure for their father sickness. Pretty sure I traumatized my SO with this one...
The whole To The Moon series hits really hard. Note that if it sounds interesting to you to see the perspective of doctors meddling with people's memories before they die (so they die on a happier memory, basically), don't watch anything major about this. Giving too much away ruins the impact.
If you are fine with the low-ish production values, the old-ish VN Katawa Shoujo works really well. Instead of showing ordinary people in extraordinary situations, it shows extraordinary people in completely ordinary situations. But as a result of how our memories of our teenage years distort with age, this works really well on adults. In particular for me, Rin's route was really good and made me cry a lot.
Disco Elysium made me cry after a short conversation with a random man on the street. I haven't played much of it yet, so I can't speak to the majority of the content, but what I have played of it evokes more emotion than any game I've ever played before.
Horizon Zero Dawn. The story itself isn't especially emotional, but learning the secret history of the world broke me, mostly because it seemed entirely plausible in our not-too-distant future.
I very rarely cry from games, but Ori and the Blind Forest made me shed a tear or two. Ori and the Will of the Wisps made my full-on ugly cry, and I was literally distraught for days.
Spiritfarer is an absolutely wonderful experience that is somehow both a casual open world chill game and a game that delves deep into the topic of death, being prepared for it, and leaving people behind. Really special game.
a world where each person only has only ten years to live and is forced to fight throughout in a never-ending war between two nations in a decaying land. There's a lot of depth surrounding the main characters, especially joint protagonist Mio who has only 3 months life remaining at the start of the story. Game gets real fucking dark.
And nah you don't need to play the first two to enjoy it, as long as you avoid the DLC expansion as that's the series conclusion.
Edit: also the most believable and well written romance between two characters I've ever seen in a game and the fantastic VA makes a huge impact (all UK talent - Mio's VA is better known for Peaky Blinders, Jenna Coleman is better known for Dr Who, for example). And anyone who says they didn't cry in chapter 5/6 is a liar.
The thread is quite large at this point, so sorry if it's been recommended already. GRIS is definitely a very emotional game. It's quite short, probably on sale quite often, visually stunning, and very sad.
It might not fit entirely in, but check out Spec Ops: The Line. It's more or less linear shooter, but the story (and ending) makes it quite unique and very different from any other game I've played. Could too get pretty emotional at times.
I played Heavy Rain and somehow managed to get the ending where everyone died. That kept me off gaming in general for quite a while. Brothers was mentioned here, I can recommend it too. Papo y Yo is a allegory of your relationship with an alcoholic abusive father, and it didn't make me cry outright but was pretty heavy.
The Vanishing of Ethan Carter! I'm not going to say anything, except that you need to do all the "side" quests. If you miss any, the map at the end will show which you missed. See the ending!
Dear Esther is also quite special, the monologues change every playthrough and everyone interprets the game differently. Very impactful.
How has A Plague Tail not been mentioned? Most of these mentioned a good games with a sad scene or two thrown in. Plague Tail, especially the sequel will make a grown man ugly cry.
You don't mind porn? Go and play the AVN Acting Lessons. It's on Steam. It's not too long but the punch it packs... it has this reputation of "the AVN you'll never wanna play again".
I like to compare it to Requiem for a Dream.
If you want less heart-rending tears, I just finished chapter 3 of Being a Dik and there were tears, but the kinda good emotional kind. I'm the first surprised, but it seems to be a signature of the author and I quite like it.
Otherwise I'm playing Metro Exodus and man, that game is oozing with that uniquely Russian despair. No tears yet, but I'm preparing for some dark moments and the whole thing is just... wow. Mad Max had beautiful everything, but M:E has fantastic writing throughout. It all feels deeply personal and with that dreadful feeling of inevitability.
And you only get to see/hear it if you want, mostly. Very glad I gave this game a second chance (it's very... clunky. Again in that typical slavic way, I guess; but it works if you accept it as it is).
My first thought is definitely Valiant Hearts: The Great War. That one, I found, to be devastatingly sad. Regularly on sale for super cheap, including right now. Also available on mobile if you prefer
Slime rancher always makes me cry at the end, but it deffo requires you reading the random notes and emails, and then also giving a shit about characters you never actually interact with. I can’t remember why it’s so emotionally effective, but this is the exact trap that keeps leading me back to replaying it and crying at the end again.
Ori and the Blind Forest? I know it's not quite as mature as some of the things suggested here, but it really knows how to hit you hard at some points throughout the story.
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.
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)
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.
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.
Disco Elysium shattered me half a dozen times. Two moments in particular made me step away from my desk and go on a walk. It's the best-written game I've ever played.
Firewatch. Gorgeous, emotionally honest game that wrings you out.
Inside. More of a stressful, cathartic cry, but it applies.
Mass Effect 3 - but only if you play the first two. Incredible story that beats you over the head with yearning .
Bastion hit me like no other game really has. The start of supergiants fantastic game repertoire and I feel it gets overlooked due to its age. The music and narration is fantastic, and the story that unfolds is beautiful.
I may be a bit late to the party but The last of us 1&2 had a pretty emotional impact on me. The game is pretty brutal, in every meaning, but the overall experience and story telling is hard to top.
I highly recommend to not get spoiled and play it in order of release!