The fire service said it had been called to more than 25 incidents following the flooding caused by heavy rain.
One woman, who lives on Carrow Road, said the water was about an inch away from her front door.
"My house is OK," she said. "I've got the towels down in preparation, but sadly the council weren't able to supply us with any sandbags."
Norfolk Fire and Rescue Service advised people not to wade into flood water, owing to the risk posed by hidden objects.
Flood water in sewers raised a drain cover near St Stephen's roundabout on the inner ring road and a car wheel jammed in the cavity.
Traffic was brought to a standstill for nearly an hour as firefighters tried to free the vehicle.
Outside the city centre, flood water made driving difficult in Sprowston and Rackheath.
People living on Hawthorne Avenue in Hellesdon grew frustrated that their road is flooded again.
One resident, Stacey Connerty, said: "Yet again it is left to local people to risk their safety to save their property and vehicles from flooding.
"This problem arises every time there is heavy rain.
"Despite repeated requests to highways and council to remedy this situation, to date nothing has been done."
There were also reports of flooding on the B1145, between Cawston and Aylsham, in Norwich Road, near to the junction with Allison Street in Marsham, at Crossdale Street in Cromer and on the A1062 at Hoveton.
Ch Insp Chris Spinks said: "Motorists should drive to the conditions and allow extra time for their journeys home.
"Standing water and heavy rainfall makes driving conditions hazardous and I would urge motorists to reduce speed, use headlights and increase the distance between you and the car in front."
Buildings and roads have been hit by flooding in Norwich.