Japan is one of the safest destinations in the world. Crime is very low. If you're female watch out for "chikan" - groping on busy trains (use the women-only carriages). Of course take all the usual sensible precautions.
We have a few more tips if you'd like some easy reading. http://journals.worldnomads.com/safetyhub/country/107/Japan
Skip past the earthquake alerts to find the good stuff.
Phil at the safety hub about 6 years ago