Oh yeah. Too many to name. First game that ever made me cry (one of my first games, generally) was FFVII when Aeris died. Cried for weeks. I had a love-hate relationship with that scene, though - I was confused. Sephi was burned into my mind as an immense bad-ass for killing her, but the death was so sad.
Crying from frustration... umm... well, I've been ganged up on by guys after they found out that I'm a female playing a FPS. Groups and hordes of guys degrading me for being female. I've only been so frustrated that I cried from them once in my life. After they burned me, I grew some balls and started talking back. The fun part about guys, they either hate you or love you for being female. I don't mean to rant - it is what it is.
Otherwise... Lost Odyssey was a close-call (almost cried). Most other Final Fantasy games or RPG's, generally. That's all that sticks out.