Your home is most likely your biggest and most valuable asset, and you should have California homeowners insurance to cover any physical damage to your home and any liability you may incur as the owner of that home.
If you have a mortgage on your house in the state of California, or for that matter, in any state, your lender will require you to purchase and maintain homeowners insurance on that home. Even if you have completely paid off the mortgage and own the house outright it is still very prudent to have a California homeowners insurance policy.
In order to qualify for a mortgage every lender will require you to have an insurance policy that will provide adequate protection against any damage or destruction to the property that they are financing. A California homeowners policy should cover all hazards as well as any liability that may occur on the property.
Mortgage companies differ in their requirements over the specific amounts of coverage you must carry, but, for the most part, they want you to carry replacement value and not actual cash value coverage. Replacement value protects the lender in the event that your home needs to be repaired or rebuilt due to a covered hazard. It pays the full cost and not the depreciated cost of the materials needed for repairs or reconstruction. Actual cash value only pays up to the limit of the policy which can be below the current market price for the materials and labor needed to actually restore the home to the same condition as it was in before the damage occurred.
Most homeowners policies in California also cover liability which protects you as the homeowner in the event someone gets injured on your property and sues. While this type of insurance is not mandatory, every homeowner that cares about protecting their house should carry personal liability coverage.