Initially when you purchase a home and have a mortgage, the bank or lender requires you to carry homeowner's insurance as part of the mortgage agreement. This is because the lender has financial interest in the home, and in the event of foreclosure if you failed to pay your mortgage payments, they would want to make sure the value of the property would remain in tact in the event of a catastrophic event.
Unlike with auto insurance, once your mortgage is paid off, you don't legally need to carry homeowner's insurance. However, cancelling your home insurance policy is a major financial decision that could be detrimental.
Think about your financial situation. Once you have your home paid off and no longer have a monthly mortgage bill, the last thing you want to do is dump the remaining of your savings and start a new mortgage for a new home in the event of a fire. Your policy covers a certain amount of personal property coverage and the cost to replace your home (depending on the type of policy and limits you have).
Don't forget liability coverage. Not only does liability protect your physical assets such as your home and contents inside of it, it protects you in the event someone gets injured while on your property. A lawsuit could easily cost you the value of your home and more.
To answer the initial question, no, you don't need homeowners insurance once your home is paid off, but the benefits of having it for a small annual premium often times make the policy worth it in the event of the unforeseen.