League of Legends Solo Queue will break you! At some point you are going to cry.

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.

I can recommend all games from SIGONO's OPUS series https://store.steampowered.com/publisher/sigono/#browse

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.

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).

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.

Yakuza 0. That ending. Bruh.

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.

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

The ending of metal gear solid three hurt me pretty good.

Try SIGNALIS ! It is extremely depressive, emotional and evocative, and to an extent it is a homage to stuff like Silent Hill 2

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.

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.

Detroit: Become Human had a really great character focused narrative where basically everyone can die. Give that one a go

Rakuen was the most recent game I played that did that for me

It was short and sweet but Planet of Lana got me in the feels a little bit.

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.

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.