When a very close one dies, usually at the funeral if somebody says something that really touches me about that person, or I see a certain picture or something else triggers it. The death itself usually does not make me cry, only very sad of the situation but certain things about the death will trigger me to cry.
I also sometimes cry if I see something really sad on TV or in a movie, but mostly if it's something real and not fiction. I saw a SPCA commercial the other day showing neglected pets and I actually cried. The commercial worked, because I got up right after and donated $50. Animal related abuse/deaths often make me cry and make me more emotional than humans, I can't really explain why.
I saddens me to think that one day my cat will pass away. My parents lost my previous cat when I lived there and I was very sad, but don't think I cried. There was a glimpse of hope that we'd find her again. We never did, but at least I knew there was a decent chance she was probably alive, but it still bugged me a lot not knowing for sure if she was in a good home, or alone. To this day I still don't know if she's alive or dead.