Some policemen are corrupt and it is usually best to avoid police interaction. Most policemen do not speak English so be willing to be polite and patient. Always carry your passport for identification purposes with photocopies of your passport, registration, and other important documents kept in a separate, safe place. Usually the police will demand to see your papers to check if you have been registered within three business days of your arrival into Moscow.
There is a deep seated racism that can be quite blatant. Non-white foreigners tend to get their papers checked frequently.
It is not unheard of to bribe police officers to get out of trouble or just ease transactions. If you run into real trouble, call your embassy immediately and explain the situation. Being drunk and disorderly can also call unwanted attention so beware when you go out.
Fire Rescue: 01
Militsia (Police): 02
(dial this number from any payphone for free) Medical Care (government):
03
Moscow Rescue Force (similar to 911 in the US): 937-9911
Lost things in metro: 222-2085
Lost documents: 200-9957 or call your embassy
Moscow Townhall Hotline: 200-6730