A little while ago I checked out the web page of the Russian consulate in NYC, and found the following text:
"Applicants who used to be citizens of the USSR or of the Russian Federation and then emigrated from the USSR or from Russia must submit one of the documents which confirms that they are no longer citizens of the Russian Federation (so called "Visa to Israel" or stamp in their passport saying that they left for "permanent residence abroad" before the 6th of February, 1992 or official document certifying that their Russian citizenship was renounced), otherwise the applications will not be accepted. A naturalization certificate is to be submitted also."
The reason I checked that page out in the first place was that an acquaintance was denied a tourist visa because her current last name happened to be different from her last name when she left the USSR in 1970-something. They figured she must be a spy or something.
The bottom line: in order to visit Russia as a tourist, I would have to show them the exit visa that the Soviet Union issued me 25 years ago, a piece of paper looking approximately like this: http://en.wikipedia.org/wiki/File:Soviet_Exit_Visa_Forever.jpg. The text I quoted above appears on so many consulate pages in so many countries that I assume the requirement is universal. One of the consulates explains that in the absence of such a document a person would have to apply to have their citizenship or lack thereof confirmed, which costs money and takes from one to six months.
I probably even have that exit visa. Or my parents have it, somewhere. OTOH, London would be a perfectly nice place for my next vacation, and British officials, for all their tendency to ask weird questions, have never asked me to prove that I am not their citizen before letting me into the country.
Yeah, I know that "bugger them, I am not going there" sounds somewhat ridiculous from a person who wasn't going there in the first place.