What things should I insure?
How's your health? Could you afford to lose it? If you become sick or disabled, temporarily or permanently, would you be able to support yourself? For most people, the answer is "no," yet a large number of people -- even some with quality health insurance -- are not insured for disability. This is foolish.
How about your life? If you were to die suddenly, what kind of financial hardship would result? Would there be dependents left without basic support? Would your burial costs impose undue hardship on others? Morbid as they are, these questions are at the root of life insurance decisions. If there are people who can't afford to lose you, you should buy life insurance.
Sometimes, you buy insurance to protect lending institutions. If you have a home mortgage or a vehicle loan, you have little choice. The lending institution will force you to get insurance and will dictate the coverage levels. In this case, it's not your financial hardship that lenders are nervous about; it's their own. You have their money, and if you can't pay them back, they'll want the car. If you've crushed the car and have no insurance, well...
In the same way, private mortgage insurance (PMI) protects the lender, not you, should you default and stick them with a house worth less than the balance of your debt.
What if you own a car, home, or other personal possessions outright? Start by thinking about which of these are the most valuable. If these valuables were damaged or lost by accident or theft, would this lead to severe financial hardship? If so, you should purchase enough insurance to replace them. Most homeowner's policies cover the loss of personal possessions. Renter's insurance does this same trick for everybody else. Auto comprehensive and collision insurance covers the loss of your transportation.
The most complicated topic among these is liability insurance. You buy this to protect yourself from others. If your negligence or error should lead to damage of their property or, worse, their health, you should be prepared to cover these costs in case you are sued. Such liability coverage usually comes with your car and home or renter's insurance. So-called "umbrella policies" are also available for more general liability. Coverage limits, in these cases, are usually based on your net worth and -- here we go again -- how much of it you can afford to lose.