As with just about any major city, watch for pickpockets around the train station, major tourist sites, street shows, etc. I watched one tourist who looked like he was just off the train in a phone booth with the Lonely Planet book in one hand, the door of the phone booth left open and a rob-me-please unzipped backpack with his camera hanging out. He almost lost the camera to a thief, but ended the phone call just before a 'helpful' hand was about to relieve him of his camera from behind.
The only thing you need to watch out for (and indeed the same in most international cities), is pickpockets, particularly in some of the more touristic areas and on the often crowded trams. One can encounter some pretty wierd people, often quite affected by some form of mind altering intake. In my experience these people look more dangerous than they ever are. They are also usually concentrated in places like the 'Red light district' where there is actually a high concentration of uniformed and plain clothed police officers. One of the safest places in the city.
Just as in all the big cities be aware for pickpockets!
And the last year there was a message in the newspaper about a guy who was robbing tourists, he saw that some people were looking on a map and offered them help (very nice of him, don't you think), he lead them to the place they want to go and offered them on the way a cookie (or something else to eat or drink) and also took one himself. Only in the cookie he gave the tourist sat some kind of drugs, they wake-up after hours without knowing where they are and without there money and camara's. He did it last year several times, so be aware!
And one other thing, if you want to try some softdrugs don't buy it on the streets, go to a coffeeshop, then you know for sure you have the good stuff.
Pick pockets. When we were in Amsterdam there was a well dressed couple that tried to steal things out of my mothers bag. Try to keep zips on bags towards you or wear your bag under your jacket and other saftey measures like that.
Keep your money and identification very close to your body! Pickpockets are horrible in Amsterdam. And if you choose to partake in a local pasttime, do your purchases at coffeeshops or smartshops. Plenty of people will offer to sell you something special. Buy it, and you might just end up spending a special night in jail--or the hospital.
Well definitely be alert of the pickpockets. If there's one city in Europe in particular that I've really felt concerned for my belongings, it's Amsterdam. Even the tram drivers constantly warn people to be careful (if you have a Dutch friend you'll have a great fun when he/she translates what the driver is saying, because most of the times they're making jokes about pickpockets). Try not to carry anything valuable in your backpack, but always on you, under your shirt, sweater, jacket or whatever. There are also words of occasional muggings (confirmed by our friends), but if you avoid the dangerous areas you should be just fine.
Be careful of Pickpockets, really just take all the precautions you would take in any city. I have seen men with the wallet very obviously in the bad pocket of their trousers - well they are just asking for problems!
I hear that Amsterdam can be very bad for pickpockets so make sure you have all your money and valuables put away and just be carefull.
By the way not even boats are safe as can be seen from this picture of the duck trying to make off with it :-)
You always hear about pickpockets, but just keep things in a money belt or under your clothes and trip around worry free! There were a few druggie weirdos hanging out one night in front of a pizza place when we were in the Red Light distrcit who looked pretty creepy. But you can find that anywhere in the US anyway. Just ignore weird people and those who try and distract you.
Beware walking around at night, especially the alleyways of Nieuwendijk - a mugger's delight. There are many junkies in the city.
Be careful with your belongings in Amsterdam. The PA system will announce that there are pickpockets at the train stations.