The Japanese have a lot of respect. When I visited a common thing said was "If you leave your wallet on the street and come back a day later, it's likely it will still be there or in the closest shop."
This actually happened. When we were living in Tokyo my wife lost her wallet. A day later she found that it was sitting in the basket of her bicycle outside our building. This was a busy street in a business district (Nihonbashi) with hundreds of people going past it and it was a large new coach wallet with at least a few hundred in cash.
Not that someone wouldn't have eventually stolen it though.
As a slightly amusing story, a very Japanese-looking American ladyfriend of mine used to live here. She's ex-military, and more than a bit of a redneck, but you couldn't tell by just looking at her.
So, one day she's on the train, and some guy cops a feel. Women here more often than not don't react to it, but ex-Navy chicks are a different story.
Mr. Pervert got decked, cursed out in English, and arrested at the next station.
Another example of this: when I lived in Japan, I used to park (and lock) my bicycle at a very crowded station and leave it there for several hours. I locked the bicycle but sometimes left my coat in the basket. I continued this habit for several weeks, until finally I left my bicycle there over the weekend while going on a trip. When I came back, the coat was gone. The bicycle was still there, of course.
That said, the most likely and annoying thing to happen to your bicycle in Japan is that the parking police will steal it if you park near a crowded place (eg. any train station) and place it in some storage facility far away from where you live, where you then have to go by bus to pick up your bicycle and cycle home. This happened to me at least 3 times..
