In USSR there was no other type of identification except passport. So obviously if you wanted to book train/flight/ship ticket, passport would be required. If you travel by car or bus, it would not be required. (I born there, so I know)
I don't want to get political on this site, but I'm still gonna shout it out: Ron Paul 2012! Tired of inflation, tired of gasoline prices (why we are at war for the oil?) tired of bs that comes out every single day! If you share my views mod it up.