Firewatch made me feel. Not quite sadness, but other strong feelings, as long as I was immersed in the story.

Valiant Hearts: The Great War. You're going to cry like a little b*tch if you'll play the game. :D :P

have you checked snoopavision? It's very sad... like very sad...

Regarding emotional great stories undertale comes to my mind first. I can't recommend that game enough. It didn't make me cry, but it made me feel a lot. Id recommend you to go in completely blind.

Binding of Isaac is also deep and emotional when you think about it.

I never cry. But these game made me almost cry;

Valiant Hearts The Great War
Life is Strange
Gothic 3 (Soundtrack)

Pacman

Final Fantasy

I cried just once for a videogame and that was to the moon :)

The Walking dead from Telltale games, both seasons.

One Way Heroics
While it may not have an outright obvious story the endings in One Way Heroics can make you cry... maybe, it did for me atleast.

Clannad

The anime made me cri evrytiem, so does the game. It's a Visual Novel tho.

G-senjou no Maou

Transistor - Whole story is strange and hard to understand but OH MY GOD that ending.
Gemini Rue and The Swapper both games after beating them will give you strong emotional hit. Not sad but more like Spec Ops The Line. You won't forget about them for long.
Dust an Elysian tale. Maybe it's not sad. There isn't anything that will make you cry but whole storyline will warm your heart. It's worth to mention that end battle have so much Star Wars in it :)
Beyond Good and Evil - Another game that will warm you heart.

If we can include consoles and emulators then
The Last of Us.
Final Fantasy Crisis Core. Especially when you didn't play FF 7
Shadow of the Colossus and Ico
Majin and the Forsaken Kingdom
Shadow Hearts 2 but you will have to beat first Shadow Heart 1 :|
Kingdom Hearts series. Especially Story about Axel. Everytime when I'm thinking how he ended in KH2 my heart is crying.

This War of Mine is the only game to ever make me feel depressed. A great game, absolutely worth playing.
The Walking Dead is pretty good too.

Mass Effect 3's ending (the extended cut version) got me pretty emotional. Okay. I admit it. I cried.

To The Moon is the only game I've ever cried to

Katawa Shoujo? Listen. I don't care what anyone says about that game. But the writing has its moments.

The Last of Us, Mass Effect 3, Bioshock Infinite, To the Moon, Telltale Game of Thrones

Although I have a bit of a tendency to cry a lot on games, I'm just gonna keep it to the few titles, that have managed to make a really special impact on me.

Metal Gear Solid

• Snake Eater Joy ;____;
• (surprisingly) Phantom Pain Mission 43 is propably the darkest and most disturbing thing Kojima's ever created
• Guns of The Patriots This one was just one big emotional hell for me. Only game I've cried on during a boss fight.

Undertale

Well OK, to be fair, I didn't really cry. I just caught something in my eye. That something was TEARS. LOTS OF THEM.

Secret of Raeticon was... something. it drew me in, in a good way, but then the ending was like the devs giving the player a giant juvenile middle finger. so pissed.

Damn.
This War Of Mine. Just playing through it keeps getting me in the feels ;_;

Games that make me sad? Less likely... Make me cried? Never ever forever :P

Bioshock 2 but only because of this ending.

http://i.imgur.com/NSej5tQ.gif

wow so many interesting games that I haven't even heard about