More commonly purchased is third party, fire and theft. This covers all third party liabilities and also covers the vehicle owner against the destruction of the vehicle by fire (whether malicious or due to a vehicle fault) and theft of the insured vehicle. It may or may not cover vandalism. This kind of insurance and the two preceding types do not cover damage to the vehicle caused by the driver or other hazards.
Auto insurance is financial protection, and not just for the investment you made when you bought your car. After a really serious accident, bills for damage and injuries can easily reach into hundreds of thousands of dollars. If you happen to cause such a wreck, the victims could sue you. In the worst case scenario, assets such as your savings and home could be seized.