The Japanese are used to earthquakes though and architecture is structured to withstand earthquakes - go for modern buildings (post 1990s).
Local authorities are prepared and have drills and exercises all the time. Rather than getting paranoid about it, you should just makes sure you are as prepared as you can be. So brush up on basic Japanese so you can understand what's going on in an emergency or get help from strangers. Also make sure you register with your embassy and make note of where local disaster shelters are.
Besides the earthquake/tsunami threat Japan is an extremely safe country and you have nothing to worry about with regards to crime - big cities will have the odd slightly dodgy red light district but in general cities are much, much safer than in say the States. Follow general common sense safety precautions and you will be absolutely fine.
As Wallace says while Japan is prone to earthquakes, the country is well equipped to deal with this threat. They have modern systems in place to detect earthquakes and tsunamis. Residents in Japan are taught how to act in the event of an earthquake, from a young age.
Don't worry too much about this when planning a move to Japan. Japan is a very safe country in general. When you are in the major cities just exercise the normal precautions that you would in your home country.
If you need some more reassurance, just take a look at the Expat Arrival's page on safety in Japan.Also, have a read of some these expat experiences of life in Japan. These interviews give you a good insight into expat life in Japan and will probably answer a lot of the questions you have at the moment.
Best of luck with your move.