I read an article in today's Los Angeles Times, by Lew Sichelman in which he talks about the need to make sure, as a homeowner, you have adequate insurance coverage.
Mortgage lenders require a basic homeowner policy to cover the property and are likely to foreclose on the borrower if they refuse to carry the insurance.
Some recommended additional insurance coverage is:
Flood. Even if you don't live in a flood area, just a few inches of water in a heavy rain season can lead to damage. Apparently the No. 1 natural disaster in the country is flooding. The National Flood Insurance Program offers insurance up to $250,000, and it is not that expensive. 
Umbrella. If you are ever sued, for whatever reason, your homeowner policy may not cover a unsuccessful outcome. To avoid losing your home there are umbrella policies that can provide you with a $1-5 million in protection over and above the limit of your other coverage.
Valuable. These can be covered with a rider on your homeowner policy. But there are limits to that. So if the value of your possessions exceeds the coverage ceiling you might consider adding a valuable-items or personal-articles floater.
Home Office. If you work out of your home, your homeowner policy may not cover your business property. What if someone injures themselves in your home. Tell your agent the details of your business to see what needs additional insurance.
Vacant Property. If you are leaving your home empty, make sure that your insurance company knows and that your coverage does not lapse.
Rental Property. If you are renting your property a homeowner's policy will not cover the it. You need landlord's coverage.
Jane, Just out of curiousity, are you able to purchase a combo policy for mud and fire out there? You know in Florida, it is becoming just about impossible to get any protection on hurricanes. What you should have, and what you can get, can sometimes be a bit tricky, now, can't it?