If you own your house outright there is always the option of not having homeowner's insurance. Many states require Homeowner's if there is a lien/loan against the property. I know in Kentucky if the house is paid off home insurance is not mandatory.
I'm not so sure it is as much the state requiring it, as it is the mortgage lender or other lien holder.
I'm not sure any state requires homeowner's insurance if the home is owned free and clear, however, some HOAs and similar developments may require it.