Japan has a low crime rate. Overall, I would say this is the country where I have felt the safest. Not to say crime doesn't happen or you don't hear stories, because you do. But generally, I think it's okay to let your guard be a little lower here.
For example, the first time I ever got my haircut in Japan, the assistant at the salon offered to take my purse before she showed me to the stylist's chair. I paused to consider the offer, then politely declined as best I could (why on earth would I let my purse out of my sight with a stranger?). Instead, I set it on the floor next to the chair. Well, as all floors in Japan are considered dirty and the customer service is impeccable, the assistant quickly rushed back over with a basket that I could put my purse in. I felt a bit self-conscious for not following protocol, and in all subsequent trips to the salon, I have let them take my purse up front. It has been been kept very clean.
Anyway, the other day, I was at a cafe near work on my lunch break, sitting outside and enjoying the pleasant weather. A woman walked up to the table across from me, set her rather large purse down, then walked inside the cafe. I was dumbfounded. I mean, I know this is a safe country, but who reserves their outdoor seating with a purse?? Utterly amazed, I counted how many people walked by (the number of potential suspects, you see) before she returned: 10. Nobody seemed to care about the abandoned purse. And as nobody but myself was sitting outside, I even took out my cell phone and blatantly framed my picture. Probably 4-5 minutes later, the woman nonchalantly returned with her latte, and sat in the empty chair across from her purse, ready to enjoy the sunshine. Now that is leaving your guard down.