Obviously this is the worst travel nightmare, but if it happens to you and even if you don’t think you are going to get any help from the local police, you have to report it to them. Only then will you have recourse in law to claim compensation from your travel insurance or contact your Embassy or the U.S. Department of State. Huffington Post contains a lot of scary stories of tourists being attacked and robbed as well as useful regional advice about how to use local resources and avoid the same problems yourself.
Before you travel make sure you have several copies of your passport. One in your carry-on, one in your suitcase, and one at home with a loved one.
Also according to the Huffington Post it is recommended that you keep the address to you accommodations in both English and the native language written in both your phone notes and a little notebook.
Get a sturdy bag. Wear your backpack facing front. Not something with a thin strap that can be broken, nor a clutch that can be grabbed, nor a wallet in a front or back pocket. My friend literally caught a woman’s hand in his pocket in a metro in Barcelona. Another friend had his backpack back pocket unzipped and things taken in Italy. If you look like a tourist (which you do), you’re a target for professionals! Check out the Travalon line of travel bags they also have metal mesh built into the straps and on the face of most of their bags.