Does your insurance cover you to drive a car that has no insurance?

Your personal auto insurance will be secondary to the insurance of the vehicle that you are driving (assuming you do not own it and it is not a business vehicle). If you get involved in a car accident while you are operating a vehicle that is -not- yours, then the insurance of that vehicle has to pay first, and if that insurance is not enough (or is not there) then your insurance will kick in. Notice that if you get pulled over by police they will ask you to show proof of insurance on the vehicle (not your insurance.) The law requires all vehicles to be insured, not individuals.