In Terry Pratchett's Discworld, there is a far off nation that is, in a lot of respects, like modern day society. The character Twoflower has a job basically giving people insurance, which is obviously a foreign concept to the people living in the lands of the medieval. He explains inn-sewer-ants (as it is written in the book) as a sort of bet. The theory is you pay somebody money, betting that something bad will happen to you, and the person you're paying bets that you'll be fine. If you lose the bet, all that ends up happening is that you go about your life completely fine, but you lost some money. If you "win" the bet, your house or car or whatever gets damaged, but you won't necessarily have to pay for it. Essentially, this means that in either scenario, you're losing.
So, insurance is basically a bet you can't win. But let me throw in a new perspective on all of this. The government legally requires me to gamble by paying insurance fees, but at the same time it's illegal to gamble until you're twenty-one (at least where I live). How stupid is that?
It's unfortunate that society is run in such a way that everything is organized to be profitable for the higher crust. I'll preface this by saying I don't have facts, and that this is simply conjecture, but I'd say the average person would save money if they didn't get insurance. If you simply saved the money you'd be paying, and waited for an emergency (like a car accident), then the infrequency of those events would mean you would always be able to pay for such things. My ignorance is probably apparent when I say such things, because maybe I'm completely wrong, or maybe my understanding of the issue is askew, but I think far too much of the modern world is built off of people taking advantage of others. Insurance is just one example, but people really suck sometimes. Don't be one of those people. Your life may be easier if you are, but I'd say most people would be happier if they tried not to be.