The two most common forms of insurance for real property include liability insurance and title insurance.
Liability insurance: provides coverage if someone is injured or harmed on your property or as a result of your ownership of the property. Typically it is sold in a package policy (renter's, homeowner's, business liability, etc.) which bundle a variety of coverage - such as liability, property contents, theft, and defense against lawsuits - to cover the risks that most owners of similar polices face. Some insurance carriers offer personal excess or "umbrella" liability policies to protect you from expose to liability risks beyond the standard limits offered through homeowner or business liability policies. Also, check your policy to see if flood, earthquake, tornadoes, hurricanes and land subsidence are covered. You may need or want additional protection if those adverse weather conditions are prevalent in your area.
Title insurance: provides coverage to a homeowner if it is discovered in the future that there was a defect in the title and the homeowner did not get clear title to the property. Generally required by the mortgage lender, this type of policy covers the costs of defending your title against the claims of another.
Commercial property insurance is more specially tailored to the type of property, loan, kind of business, etc..