I think other than health or life insurance, two other importance types of insurance are home insurance and car insurance. That is, of course, if you have your own car and house. If not, then you don't have to worry about both!
Having lived in a small alley in Bandung made my Dad insure our house for fire or natural disasters. If a fire started in one house, it would spread pretty quickly to the other houses. And since the fire truck wouldn't be able to pass by the small alley, it would take a while before the firemen could put it off. Dad always says, "It's much better to pay some money per year to make sure that if something bad happens, we're not going to lose everything. We'll get something in return for the loss." That's his way of taking care of my family.
And since car theft is also a big issue in Indonesia, when Dad still owned a car, even though it was an old car, he insured it. Of course he had to compare car insurance programs first to make sure he got the best deal. However, now that he's sold the car, he doesn't have to worry anymore about getting his car stolen! All he has to do now is keep on insuring the house.