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.
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.
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.
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