I'd love to go out of curiosity, although I gather it could be a bit dodgy i.e. foreigners have to report to the local police station when visiting.
Actually, the same system exists in much of Europe, except you don't see it. For instance, in Schengen countries, the police will routinely visit accommodation providers to find out who's staying - and in some countries, it's reported automatically. Croatia has the same system too - and foreigners do get fined for failing to register.
Anyway, I have some Belarusian friends, and they tell me the same thing - as long as you don't go looking for trouble, Belarus is a safe country.