Embassies maintain a list of travel warnings for Japan. Check with your embassy for the latest warnings.
That being said, Kabukicho (in Shinjuku) and Roppongi are often cited as Tokyo's more dangerous neighborhoods.
In 2009, the American Embassy warned all of its citizens not to go to bars in Roppongi. Numerous bars in the area were spiking customer's drinks and stealing their wallets. In other cases, customers are presented with outrageous bills (thousands of dollars for one drink) and forced to pay by large bouncers.
Similar scams have been reported in Kabukicho.
In many cases, the victims were brought to the bars by touts they met on the streets. In other cases, they were brought to the scam bar by attractive women they met in regular clubs.