@Tanuki's answer is an important one to note, there has been many incidents like these in Shinjuku area.
There are other small scams that I have seen, but these are minor:
- There are some people who are hanging around the entrance of Ueno Park and raising funds for earthquake victims. Usually, fund raisers get a permit from the police and stay at one location. But these people stay within the crowd, and have been collecting for ages. I am not sure if they are genuine or not.
- In busy stations of Tokyo, a well-dressed middle aged person might tell you that he lost hist wallet in the train and ask you for money to get home. Japanese police boxes lend money for people in such cases; this guy just targets foreigners who are more likely unaware of this. I recently noted some foreigners (looked like they are from China) playing the same trick on other foreigners.