odudog

The bowing is to show respect. It is also to show hierarchy. If you were to see two Japanese people out in public, you would know which person has the higher status for that person did not bow as low as the other person. It is also a show of trust by the lower status person for his/her neck is being more exposed and he/she can't see what the higher status person is doing. It is also a personal space issue. Japanese {more so the old days} tend not to be too touchy feely and the bow is a way of showing respect, gratitude, and status yet maintain your own space. Also good for personal hygene.
I think the Muslims must touch their forehead to the ground when they bow to show their submission, however, in the Japanese bow you never touch your forehead to the ground. It might be close to show deep regret, but it will still never touch the ground.