Japan is often raved about of being one of the safest countries in the world. While this is not exactly true, Japan is definitely a very safe place to live in.
The United States has an estimated 4 times higher crime rate than Japan, and even in the big cities the chances of you becoming a victim of crime is highly unlikely. You can leave your bicycle unlocked, your bag at a public table in a restaurant, and even drop your wallet on the ground and not have any of those stolen. People will usually go out of their way to return a wallet that you have left behind somewhere. This idea of honesty is ingrained into most Japanese people.
Japan does have a lot of petty crime though. People will mainly steal umbrellas that have been left in an umbrella stand outside a store, or occasionally steal a bicycle if it’s nice. I have never had my own bicycles stolen, but I have a friend who has had his stolen from his apartment complex bicycle parking area. He started locking his new bike every time from that moment on.
Violent crimes such as murder are extremely rare. Rape rates are also very low, with the US having 27 times more reported cases than Japan, but these statistics can be deceiving. Rape is underreported in both countries, and most cases of rape are not even recognized in Japan when they are reported. Domestic violence is a very delicate and private issue, so victims of abuse by family members are unlikely to report their assailant, and will probably not even be heard if they do. Japan takes diligent action with many crimes, but this area is sadly one that needs improvement.
Since guns and most knives are illegal to own or carry around, rates of violent crime involving weapons are astronomically low. Walking down the dark streets of Tokyo at night feel extremely safe. You will likely never be bothered. I would say the most you have to worry about is your bike, where you park it, and maybe the scammers that try to get a “donation” from you for some charity outside a busy station.