Insurance companies work hard to ensure that, at least on the average, they are going to take in more than they pay out. I believe that they are good at that, so I make it a point to only insure myself against potentially life changing expenses.
I have homeowner's insurance, health insurance, car liability insurance, and an umbrella policy because a fire, a cancer diagnosis, or a lawsuit might change my family's financial situation if I had to pay out of pocket. I can afford to replace my car if it is stolen or wrecked, so I don't pay for comprehensive or collision. I have an extremely high deductible on my homeowner's insurance, but I have more than enough money in my emergency fund to cover repairs up to the cost of the deductible.
If you can't afford to replace things, you need to insure them. The more money you have, the higher your deductible can (and probably should) be, and the less you need most kinds of insurance.
Insurance is one of several areas where being FI saves you money.