Sad games

Clannad made me cry like a baby. If you are into Visual Novels I highly recommend it. Be warned though, it's huge. Takes dozens of hours to complete every path (and to unlock the "true ending" you need to play through every other route), the pace is really slow at times, art style is dated and characters look weird. Gotta admit I dropped it after completing couple of routes and needed few months break to get back into the game, but in the end I don't regret playing it and I consider it one of the best VNs.

Valiant Hearts
Life is Strange
To the Moon
Last Day of June

I guess I can't add anything anymore, every sad game I can think of has been mentioned already, but I have to admit, I'm quite emotional if I like a game, so it's rather easy to make me cry, or feel sad ^^"
I cried at the end of Life is Strange and when I finished Bioshock, I was really sad at the End of the Deponia trilogy (although it was a good kind of sadness ^^), I was moved when I finished Caligo and Empathy: Path of Whispers made me think about so many things...
Oh wait O_O I guess no one mentioned Old Man's Journey jet! It's such a great and sad game T_T
http://store.steampowered.com/app/581270/Old_Mans_Journey/

I'll just quote RPS:

"The last time we saw The Walking Dead it was lying in a pool of blood, waiting to rise again as some sort of brain-hungry second season. The bastard game hadn't so much jerked the tears from my eyes as attached wild horses to the ducts and had the muscular beasts run toward the horizon for a couple of hours."
     -- Adam Smith

I want to add one that's a bit surprising: Child of Light. While it's a bright, cheerful looking game akin of the standard fairy tales of fighting the darkness, the game's music (strings, piano, wind instruments and drums) is such a perfect fit for it that it really amplifies the tone. I'm not super fond of turn based combat and it's basically a child's story, but the game's darkening tones (one of the musics is called Hope is Low) really makes one invested in the game - for some reason this was the first game in a long, long time where I really felt like making a last stand against darkness and trying to save the world.
Not necessarily sad-sad, but really emotionally charged, and very well made game.

Life is Strange- the first game

Sometimes: Borderlands 2 withTiny Tina Assault on Dragon Keep DLC (but it's better to first end main storyline before that one).
Kane and Lynch: Dead Man - things don't go well for protagonists.
Kane and Lynch 2: Dog Days - downward spiral continues.
199X - quite short one, but with sad atmosphere.

Ori and the Blind Forest because you'll be sad that you've finished playing this absolutely fantastic game.

All jokes aside, I don't know about "sad" but Lucid9 made me feel some rather confusing, mixed emotions, mostly because I really got into the twisty story that keeps you on your toes until the very, very end.

SOMA is also a good pick for games which have a rather sad setting and overall outcome, although again it's mostly playing with your emotions by keeping you confused, wondering. Fantastic game overall, with a theme I was already interested about in the past so that's a plus - It's possible I just got too much into the game hence my emotions being played with.

The Vanishing of Ethan Carter was confusing, but kind of sad in the end if you manage to piece the story together. Still not sure about how exactly the story unfolds.

Eternal Senia unexpectedly hit me in the feels pretty hard, since I wasn't expecting any story to this game (I played it almost upon release, so nearly no reviews). Great, simple RPGMaker game.

Oxenfree isn't sad, but played with my emotions a lot. Wasn't expecting such a rollercoaster.

Papo & Yo simple, fun game... until you realize what the fuck is going on.

DayZ
U will cry how its incomplete in milion years of making :D
It would be great game but they wasted chance with epic slowpoke style... X years and still alpha

Haven't seen anyone mention Transistor yet.
Oh, also, just played a short Chinese indie game called Don't Disturb, which is all about mourning. The incredibly Chinglish text luckily does not affect it much, it is mostly visual.

Though it's as a whole quite a bit more weird than sad, Doki Doki Literature Club does pack a small collection of heavy emotional punches.