Never get into a taxi carrying anyone other than the driver. Look at the driver and condition of the car. When in doubt, wave the taxi on. Taxis ordered by phone or through organized services at hotels are often a best bet. Never give your home address to a stranger.
Foreigners are even better targets for thieves.
Don't show large amounts of money, especially hard currency. For small purchases, carry some rubles in one pocket and some dollars in another. Carry your documents and large sums of money separately inside your clothing in a money belt or pouch hung around your neck. Safest at currency exchange offices. Stay away from Gostinyy Dvor and Apraksin Dvor.