With a population of about 12 million, you can expect the same safety risks in Moscow that you would in any major Western city. Don’t make flashy displays of cash, and keep your wallet, camera, or other valuables out of sight. Take precautions against pickpockets in crowded public places, including public transportation.
Ethnic minorities, or those perceived as such, which often include Caucasians with a dark complexion, should be aware of somewhat heightened risks from groups of nationalistic youth. They also face more frequent random identification checks by police and possibly a lesser chance of police assistance in case of harassment.
Moscow has a reputation for racially motivated skinhead violence and you will find an endless supply of anecdotal evidence which supports this. However, the vast majority of the population of Moscow are law abiding and you should be safe if you follow a few rules of thumb. For example, don’t provoke bands of teenagers, avoid people who appear homeless and/or intoxicated, don’t insult the soccer team of a group of drunk fans and avoid walking or traveling alone in the city late at night, especially if you are a woman or an ethnic minority.
Gay women and especially men should avoid public displays of affection completely, out of interest for personal safety.
It is wise to take additional precautions and avoid public gatherings on April 20th, which is Adolf Hitler’s birthday; November 7th, which is the anniversary of the October revolution; and dates of major soccer matches for Russia. On these days, groups of young radicals and nationalists are most likely to be out and about, and drunk.
Finally, never open your front door to anyone you don’t know. This includes the police who may have received information that you are foreign and be attempting to elicit a bribe under the pretense of a ‘noise complaint’. Simply ignore them and if they persist call your employer who will be able to send a witness and make sure proper procedures are followed.
Because Moscow is often considered unsafe by foreigners, many employers will employ a security organization (such as MIG http://www.mig.ru/en.html) which supplies emergency assistance to their foreign employees. They can be called in case of anything from a picked-pocket to police harassment.