Amsterdam is a major urban area and is at least as safe as other major European cities.  Violent street crime is virtually unheard of. That said, always be aware of where your valuables are.  As in all crowded situations men should keep their wallets in their front pockets.  Women should have a good hold on their handbags. Pickpockets do work the train station (Centraal Station), the trains back and forth to the airport, trams, and crowded areas.   Make sure your other valuables, i.e., cell phones, iPods, cameras, etc, aren't hanging out there to be snatched by passers by.

In the Red Light District, do not attempt to take pictures of the women on display in the windows because somebody is bound to harass you or even take your camera.  If you think nobody is watching you, you are wrong.  They have eyes everywhere which you never notice.  Be respectful.