There could be so many answers to this. You could just be an emotional person or you could be mildly depressed. It depends on what type of music your listening too. Crying over certain songs is not a bad thing. I do it all the time and it's usually because it brings back memories, some good some not so good. No, this does not mean there is necessarily something wrong with you. You didn't say how long this has been going on, what type of music it is or anything that is or has been going on in your life, past or present. I know this probably doesn't help much but at least you know your not the only one with this issue.