The Walking Dead, Gone Home, Final Fantasy VII and Homesick.

This War of Mine, when you play the first game (quite random setup)
Fallout NV with the DUST mod (well, I had some 140 mods...)

Thomas Was Alone. Had tears in my eyes at the end. The music is very emotional.

Shadow of the Colossus. Personally, I couldn't care less about Yorda, but when something happened to Agro, I was pretty down. Also, I've never felt so heroic when mounting that flying bird colossus at the water stage.

Grand Theft Auto V: This game was difficult for me to play because of Michael. His character reflected lots of sentiments I have about my life and situation as a father and husband. Michael is almost my spirit animal, for he echoed my thoughts on many things when it comes to family and life not turning out the way you wanted it to.

Wolfenstien: The New Order: This game has depth of character for a main that I haven't felt in years. Yes, its a dumb FPS but its the story and cast of actors who brought the characters alive. From BJ to Bombast, these are living people in a universe that is oppressive and heavy. The ending credit song in particular is a moving tribute to the events of the game and of BJ's mental state through out the game.

Limbo: This game made me bawl when I realized what had happened to the main.

Bioshock: That tiny ending made me bawl for almost an hour, the good ending. Seeing the fragile hands on Jacks as he was dying drove the point home that rescuing the little girls was the path to go.

Metal Gear Solid series had moments where I would feel a range of emotions from pure rage to utter disgust, and that is what art is meant to do. Ground Zeroes alone is full of moments where you want to just murder everyone responsible for the site.

Other notable mentions: Spec Ops: The Line, Among the Sleep, El Matador (the ending sequences when the truth is revealed will make you want to crush your keyboard), and many others. Not just tears, but pure emotions like anger, rage, and elation are always present in good games.

ok, not quite about the game itself (tho it has its moments :) ) but this, Elizabeth casting, I watched it before the game be released, it doesn't (probably) make you cry, but emotional, sure I think so! I mean, I got the chills by watching her performance.

YT video, about min 6

I should say that I was moved the first time I've played MGS and the whole Meryl thing. Also what became of GrayFox..
I bet there are more times when you're mad and want to trash everything, than those times when you empathise so much with the chars and/or what happens to them, makes you sad and then happy and maybe sad again :P Those linger more, in time. We need more of that.

The ending of Final Fantasy XII-2 got me ;-;

Fahrenheit
Mass effect 2

Not mentioned so far: Dishonored, Deus Ex: HR, The Stanley Parable, The Wolf Among Us, Transistor, Papers Please.

Bastion, Transistor and To the Moon.

For me, To the Moon and The Walking Dead (season 2).

LISA.

Sad and funny at the same time. Dark humour tho, really like the mix with the dark humour and the depressing sadness.

The beginning of Ori and the Blind Forest.
I had just started the game, and I was already bawling like a baby by time the game really started.

Well first of all... I am someone difficult to get emotional. But there are a few games that really messed with my head emotionally and or made me cry.

The beginning and the ending of The Last of Us blew me away emotionally and both scenes made me cry as well. It's on PS3 and PS4 though.

Spec Ops the Line is a great one too. Really messed with my head and made me question my choices excessively. It's on Steam. Pick it up!

Deadly Premonition is the best one in my opinion. Deadly Premonition is my number one favorite video game of all time. Beat it on Xbox and PS3. Grabbed a copy for PC too. Anyway. Deadly Premonition has A LOT of emotional "what the heck" moments and has a lot of amazing characters that will attach to you emotionally. The story is mind-blowing awesome. I cried a few times playing that game. Deadly Premonition Director's Cut is on Steam too.

The last of us - and not because of ending... just prologue was enough
Walking Dead from Telltale - ending was so emotional (but stupid in some moments :P )

The 仙剑奇侠传 and 轩辕剑 game series.

Call me crazy, but I'm gonna go with Shadow Warrior (2013 reboot).

To The Moon, This War of Mine & The Walking Dead

The feels are real T_T

I actually shed a tear at the ending of Portal 2. It was too beautiful and emotional.

Also, do you guys think that it's worth getting LISA for 5€?

Mother/Earthbound saga.

LIFE

Bioshock series
Mafia 2- That ending was so emotional, its leaving me wanting a third one and if you play, youll see why
L.A. Noire
Star wars Kotor 2
The walking dead series

a lot of games but for me i think it was mass effect 3 the end destroyed me i mean you play 3 games you explore this vast and epic game and it end brutally :/

Crisis Core: Final Fantasy VII

Mafia II

GTA V

GTA IV

Red Dead Redemption.

Oh, I talked about The Cat Lady but completely forgot about Red Dead Redemption. Other one from my favorite games from all the time.

I still dream about the day that it will be released on PC. :(

Seeing as we're also doing non-PC games too :
Ghost Trick.