I've been asked to show my hotel reservations when entering China and I've watched the person in front of me find the hotel confirmation to enter Argentina. I don't recall specifics, but I would expect Russia to ask for the hotel reservation and, in fact, it's possible that they could do this when you exit the country.

Some foreign airports ask where you stayed as part of the security question about where your luggage was packed. I've seen airport security employees ask for documentation that the passenger did indeed stay in the hotel that was named, although presumably a bill would be better than the reservation for this purpose.