One of the first things a professor/instructor in Insurance Law said, and incidentally the only thing I remember from that course, was "The first rule of insurance companies is 'Don't Pay!'" Litigation would arise from this refusal in a small number of cases, bearing in mind that the cost of litigation would be more than most household and even travel claims, saving the most extreme. I suppose that's why I've always been wary of insurance policies.
You have to have fire insurance on your home. Probably your mortgage company requires it. House fires in owner occupied homes are not very common but just in case . . . You couldn't sleep at night without it. What about a robbery claim? Those are more common. A young person broke in and stole our stereo and video recorder many years ago. If you ever make a claim be prepared to have your premium go up the following year and not just on that property but any other real estate (like an investment condominium) that you happen to own. Don't forget you'll need to pay the deductible ($500 to $1000) first. Before long you've paid for your replacement item yourself.
Some people take out disability insurance. It seems you are more likely to become disabled, than die, at least in the short term. But what is disabled? If if you became a quadriplegic, unable to use all four of your limbs, your insurer might think that you might be able to hold a pencil between your teeth and tap out letters on a keyboard with the eraser end. A little research on-line turns up a lot of sad stories. Some are satisfied with what the insurance company has provided. It can make you feel that paying a monthly disability premium was a little like buying a slew of lottery tickets every month. You hope, you hope.