I can get very involved in a story, if it is a compelling one. In a well-acted, well-written movie, TV show, or stage play/musical, at a particularly moving moment, I've been known to cry. The worst was years ago when I saw the show Les Miserables. That scene at the barricades? OMG. It was an incredible struggle to keep from just bawling my head off.
On the other hand, when it comes to REAL LIFE... I can't remember a time I've really cried since I was a kid. I'm sure the time will come, though.