The crime rate is very low, and the conviction rate for serious crimes is very high. Critics will point out that a large number of crimes go unreported, and most convictions are based on confessions (Japanese police can hold a suspect for up to 25 days before filing a formal indictment. See Arrested in Japan). However, many foreigners in Japan say they feel safer here than they do back home.
It is still important to take precautions. One crime that occurs enough is theft. Be it umbrellas or bicycles, cash or computers, there are plenty of people who help themselves to what they can. So tell all of your family back home how safe it is here, but lock your house, lock your bike, and don't leave your wallet lying around. You know, common sense.
Here are some general tips & facts:

  • Yakuza do not interfere in the daily lives or activities of average people, unless you are involved in criminal or shady activity.
  • Statistically, Japan is one of the safest countries in the world, even though a lot of "minor" crimes are under-reported.
  • Train gropings and underwear thieves are 2 of the common crimes which occur to women. However, recently young women have been becoming more aggressive in defending themselves and reporting such crimes. There are also "women only" train cars during rush hour on most crowded train lines in major cities.
  • There have been some high profile murders of foreign women by stalkers, but shocking as these cases may be, the actual number of incidents like this are very very low.

REMEMBER: As long as you keep yourself alert, aware of your surroundings, and take simple safety precautions, you will find Japan to be an extremely safe country.