Property Insurance
One type of policy that for most people that is actually mandatory to have is homeowners insurance when you have a mortgage. If you borrow money from the bank to purchase a home they will require the asset to be insured. For many people this insurance premium is built into the mortgage payment. For many people their home is their greatest asset so it is vital to adequately protect it.
If you rent instead of own, a renters insurance policy is just as important. Your belongings inside the dwelling can add up to a significant amount of money. In the event of a burglary, fire or disaster you should be able to at least have a policy that can cover most of the replacement costs.
Consider also buying liability insurance which covers you if someone sustains an injury or other loss on your property.
Renters and condominium owners need only contents and possibly liability insurance. Many companies have policies tailored to these purposes.