Any risk that can be quantified can potentially be insured. Specific kinds of risk that may give rise to claims are known as "perils". An insurance policy will set out in detail which perils are covered by the policy and which are not. Below are (non-exhaustive) lists of the many different types of insurance that exist. A single policy may cover risks in one or more of the categories set forth below. For example, auto insurance would typically cover both property risk (covering the risk of theft or damage to the car) and liability risk (covering legal claims from causing an accident). A homeowner's insurance policy in the U.S. typically includes property insurance covering damage to the home and the owner's belongings, liability insurance covering certain legal claims against the owner, and even a small amount of health insurance for medical expenses of guests who are injured on the owner's property.

Business insurance can be any kind of insurance that protects businesses against risks. Some principal subtypes of business insurance are (a) the various kinds of professional liability insurance, also called professional indemnity insurance, which are discussed below under that name; and (b) the business owners policy (BOP), which bundles into one policy many of the kinds of coverage that a business owner needs, in a way analogous to how homeowners insurance bundles the coverages that a homeowner needs