Even in its major cities Japan is a very safe country, with one of the lowest crime rates in the world. You should, however, keep an eye out for pickpockets and avoid unlighted roads at night like anywhere else. Distribute your cash, credit cards, IDs, and other valuables between a deep front pocket, an inside jacket or vest pocket, and a hidden money pouch. Don't reach for the money pouch once you're in public.
The greatest danger is being caught in an earthquake and its resulting tsunami. Earthquake information is broadcast (in Japanese) as news flashes on television within minutes, and during major disasters national broadcaster N.H.K. broadcasts information in English on radio and television. Minor tremors occur every month, and sometimes train service is temporarily halted. Check emergency routes at hotels and higher ground if staying near coastal areas.