Most importantly, don't ever remove your wallet on the street in Russia unless asked to do so by an accredited authority source. You'd be surprised to hear the ingenius methods locals have come up with for getting foreigners to take out their billfolds or passports, at which point they promptly demand them or snatch them.
Do also realise that extortion is a common problem. Police officers and traffic cops are not your friends. If they do demand money from you, and you feel the demand is unjust, be sure to get their badge number and ask to speak to their superior before you give up. In many cases this will change their demands.
Otherwise, take common security precautions, and try your best to blend in.
For a more detailed overview, read the Expat Arrivals safety in Russia page.