I actually was never carrying an ID while walking down the streets in Russia - in most cases this is not needed, and it is not compulsory by law. If you travel by train or air, you must have an ID with you - but in the USA, you also need an ID to travel by air, do not you? The police have the right to request your ID only if you are a crime suspect. I believe this is the same in the USA, isn't it? The problem is that this right is easy to abuse. In Russia, especially in bigger cities, policemen can claim you resemble someone wanted, and place you in custody until your identity is determined (but not longer than for some time which I do not remember now). They would release you from custody for a small amount of money unofficially paid to them. The problem is thus not in the law, but in the improper conduct of policemen. Identity cards or passports are compulsory in many countries, see List_of_identity_card_policies_by_country. The USA is more like an exception, actually.