I think I have actually cried 2-3 times thanks to a videogame (I cried because of Lair but in another way...) though it depends on if I'm alone or not. (Boys don't cry!)
I cried when Ocarina of Time was over.

I think Aeris' death made me cry but I can't remember...

Terranigma ending scene. A very simple ending but...Ah, you have to play it to understand

Snake Eater almost made me cry.

I'm still waiting for a game to conquer Chrono Crusade though. My God, I cried like a baby when I saw the anime. Then I read the manga and was like "I know they're going to die. I wont cry this time...". 2 chapters left. Me crying like 3 babies.

Final Fantasy VIII - When Rinoa almost dies in space
Final Fantasy X - Ending
Ratchet & Clank: TOD - Constantly throughout but this was due to laughter
Bioshock - Ending (good one)

MGS4 has to be one of the most touching games I've ever played. I didn't cry, I just felt empty inside, that kind of feeling when your heart is filled with tension.

SPOILERS!

MGS4:

Microwave scene. Damn thought Snake was gonna die and I kept stamping on that triangle button, and it was really hard watching snake getting tortured in that room.

Visiting Shadow Moses. This brought back instant memories of me playing MGS1, and I felt so sad because it was that kinda nostalgia feeling that overtook me.

The ending. As DarthDevidem said, the scene when Otacon is talking to Sunny and he is actually crying thinking that Snake is dead. He's trying to hide he feelings but he has to let it out and at that same time he is still trying to hide it buy turning away. This had to be the scene that almost got me to cry, because at that time we all thought that the hero who saved the world, Solid Snake, was gone.

Those are just a few of the very touching moments in MGS4. And I'm afraid we aren't going to see any game as great as MGS4 for a long, long time.