I've lived and traveled all over China for three years, and not once have I ever had an official, police or otherwise, ask me for any type of identification on the street or in my residence. 

However, when I check into a hotel, buy tickets, or travel on a train, I do have to show my passport. In plane travel, obviously, they check it at the security station in the airport.

They came by my apartment once but not because Im foreign. In some types of apartment buildings, they go around to check who is living there, and also if too many people are living in one place.

They were nice and just asked for my passport and how many people lived here. Then they went on to the next door.