Metal Gear Solid 3 - It's been nearly a decade, I've seen it probably 15 times, and I still choke up just hearing the music. One of the truest, non-jingoistic expressions of patriotism (I don't care where you're from, still true) I've ever seen.
Bioshock Infinite - this game made me want to have children. True story. There's a moment near the end where Elizabeth is put in pain and... well, I'd never felt actual, genuine rage at a fictional character before. I executed the Comstock House surgeons for daring to put their hands on my girl. To have that ending after that kind of attachment... I'm still not sure if I'm heartbroken, or thrilled.
Final Fantasy X - I know, I know. But if you can get past the weird Japanese fashion sense, there's a fantastic classical tragedy underlying the game. I cried for the end, but came pretty close at the Sending and the spring too.
Shadow of the Colossus - I don't really know the reason with this one. It was powerful, sure, but not sad... Then again neither was BSI, really. I think the game just did a great job of drawing me into the character so I felt it more.
That's actually pretty impressive evidence for the power of games as a medium, actually, since the only movie that's ever done me in to tears was Black Hawk Down (oh god the music 0_0)