I can honestly say there have only been a couple times where I have been "emotionally touched" whilst playing video games. The first was (yes, sad I know) Super Metroid. After 70+ hours of playing, it was a combination of being saved by the metroid, the awesome boss battle with awesome boss battle music and the escape to your ship.
Another time was when I was playing Shadow of Colossus, the vast landscapes and massive enemies was so breathtaking at the time (and still is) you just couldnt help but get a bit emotional. It takes a very good development team to produce a video game which pulls on your emotional strings, movies can do so quite easily but with video games you have to give the dev team a lot of respect when that happens.