Japan is one of the safest countries in the world.  There is virtually no threat of being mugged, assaulted or robbed, assuming one uses common sense and doesn't go looking for trouble.  This is not to say that Japan is crime free or free of violent crime.

Pickpockets are always a threat in crowded metropolitan areas and Tokyo is no different.  Use common sense regarding carrying cash, valuables and important travel documents and almost all problems will be most certainly avoided.  For men, this means carrying wallets in a front pocket and for women, carrying wallets in a sealed and secure handbag.  While the lore of Japan is that a bag of cash left on a park bench is likely to be returned (this is true) there are exceptions to this rule and there is no value in testing it.

Burglary has become more commonplace in residential areas where it is no longer safe to leave a home unlocked when not there.  It's usually transients passing through neighborhoods perpetrating this sort of theft but it pays to be careful, just in case.   When staying in major hotels, the chance of theft is very slim but use the room safe or a safety deposit box at the front desk to store valuables.

With the small influx of undocumented foreign residents into Japan, more and more scams and swindles are being seen in the major areas of Tokyo.  Just ignore these people and avoid any offers and enticements you may encounter.