When your car is totaled, the insurance company has an obligation to "make you whole," as that is defined in the policy.

Most policies value your vehicle using Actual Cash Value. "Actual Cash Value" means replacement value less depreciation.

This essentially means you have to be left in approximately the same financial position (with respect to the item insured - not in respect to any liens or leases that hold title to your car) you were in before the accident.

If you have physical damage coverage (comprehensive and collision) the insurance company will typically write you a check for the actual cash value of the vehicle, minus any deductible on your policy. If you are "upside down" on your loan or the cash value is less than your current loan amount ("Upside down" means owing more on a car than it's worth.) then you should consider GAP insurance. In this situation, if you don't have GAP insurance then you would be responsible toward your loan for the remaining balance. The terms of that payment are set through you loan contract.

Comment Update: Please see our related answer titled: How is the "actual cash value" determined?. This should answer your additional questions. It is the same in Arizona as in other states.