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If you've got the time, the money, and the right attitude, I'd say a month at least. I wouldn't exactly equate a stay longer than two weeks with "moving" to Japan, but you certainly can get a deeper understanding of what daily Japanese life is like if you stay for a longer period of time, rather than just riding that wave of tourist euphoria that you get your first week or two there. As Nyororin said, it really depends on the person. My first time to Japan was an extended stay, and I felt very little culture shock, and I felt like I could have stayed even longer than I did (a month), but on the other hand, I've known people who simply can't deal with the "normal" Japanese lifestyle, and wouldn't be able to stay longer than the average tourist does. I watched a person have a mental breakdown by their third week of studying abroad in Japan and had to go home, just because she didn't 'click' with Japanese society very well.

So, I'd go with the following conclusion: if the person likes to travel and just wants to "see Japan", then make it two weeks, simple. But if the person has a desire to live in Japan in the future, I'd say stay as long as they can, because wandering around Buddhist temples or Akihabara isn't going to prepare someone for living there - they have to see how well they deal with daily life there.