Local police & Documents, Moscow
Always carry your passport at all time. The Miltia will do thier thing cause they can. It is one of the things I disliked about Russia. It is funny when they start talking to you in Russian and they are holding your US passport. Like you know what the hell they are saying. Funny actually. We got stopped 4 times just because. That is how it is there. They like to show the power. I understand bribes are excepted readily though I just gave them the stare down and that worked. A hassle really. Also never drink the water anywhere in Moscow. Always drink bottled water. I brought my own for brushing my teeth. I hear that you can get pretty sick from the water there.
The police check your passport and visa's regularly. Be sure the hotel registers your visa, or you will be charged a fine. Like any big city watch where and when you go places. Night time is the most dangerous, but I had no problems, wandering about the city in the daytime with my street map. Just use common sense.