Yes, many times. Despite my emotional disconnect, i have cried over many games. Kingdom Hearts, Final Fantasy X, Professor Layton and the Unwound Future, just to name a few.
Having replayed the entire Kingdom Hearts series recently, let me tell you, every time Simple and Clean plays, I get choked up, and this is due to the end of Kingdom Hearts 1. That ending gets me every time. They start Simple and Clean at just the right moment to hit me right in the feels, and now I'm like Pavlov's dog, I respond a certain way whenever I hear it play in one of the games.
I haven't replayed FFX yet, so I don't know if it'll still be an emotional moment for me, but when I first beat it, it was one of the first games I'd played on a Playstation console(I had an N64 and couldn't afford to also get a PS1). The graphics for me were astounding, the voice acting was brilliant, the atmosphere perfect, and the ending, when Tidus fades away was one of the saddest things I've ever witnessed.
Professor Layton. This is one of the more recent games that has made me cry. The ending to that one particular game is just heart-wrenching. I don't want to spoil anything for those who haven't played it, but damn did I cry.
There are other games, of course. But these three are the ones that effected me strongly enough that I remember exactly what about them made me cry.