Certain countries require you to carry your passport while travelling
Always carry your Hotel's visiting card in such countries + copy of your passport on your phone.
*If* a Policeman is feeling funny, show him your Hotel's card and ask him to verify your credentials.
Worst case scenario (in some CIS country or parts of Africa), you should insist on being taken to the Police station where your antecedents can easily be verified by the hotel.
*Under no circumstances should anyone ever carry original passport on-person*
