I believe people are basically good. I have met very few malicious individuals in my life, and normally when someone does something horrible, it is because of messed up incentives. In economics, a moral hazard is when someone takes more risks because someone else is bearing the cost of those risks. So if you have insured something, you take less care of it. If everyone does that the cost of the insurance skyrockets. Since insurance companies are big and impersonal, 'they' will bear the cost.
In claiming, normally honest people will exaggerate in order to even the scales. So if 70 DVDs are stolen, they may claim for 100 because they think the insurer won't pay for the full claim. Others may even justify stealing because the individuals will be insured.
A combination of moral hazard and the fact that insurance companies do need to make a profit means that I follow a policy of accepting the bumps. Take insurance out for things that will completely blow you out of the water, otherwise accept the risks yourself. One of the first forms of insurance was for the Merchant Ships. If you owned a ship and it didn't make it, that was the end of you. If there were 10 ship owners and they each agreed to cover each other, if 1/10 ships sank, each Merchant could take a small hit but stay in business.
Most people's biggest asset is their ability to earn an income. The most important form of insurance in my eyes is Disability Cover. If you can't earn, it is a big problem. If you die, it is not a problem... for you. If you have dependants, that is different. Then you are making sure they don't get blown out of the water, so Life Insurance matters.
We don't need to protect against all risks. Bumps aren't bad. Bumps are part of life. Bumps also make sure we have the skin in the game to play nice.