The first time a game legitimately made me cry was when I played Red Dead Redemption, and got to the final level of the game.
Watching something that I'd busted my ass to build for a genuinely interesting character break to pieces because of the whims of evil men hurt me on a deep level, as did John's response to the whole situation. I think the point where I actually shed a tear was when at one point, I heard John shout "I did what you wanted!"
If we're talking about like, actually breaking down crying...
Okay, fuck it. I'll powerlevel a bit. My mother died when I was 9. She was a huge fan of Final Fantasy, and she had an old Playstation, and the full sets for FF7, FF8, and FF9, plus Xenogears which was some BALLER SHIT. Anyway, her favorite was by far 8, and even though we had a newer Xbox and PS2, she always kept the PS1 hooked up in the living room so she could unwind and play some after she got back from work. Since she was a teacher, though, she never really had time to get very far, and often she'd end up restarting the game because she'd have gone a month or so without being able to really play because her students weren't meeting the school's standards, or such. My stepdad was a pretty big fan of the games, and he ended up beating all three, but my mom never really got any farther than Disc 2 of FF8.
When I was 19, I saw Final Fantasy 8 on sale on Steam. I bought it . I had just dropped out of college, and I was in the middle of a depressive death spiral, so I was already not in the best space. It took a couple of weeks, but I beat the game.
The moment the credits started rolling, I started crying.