No states require comprehensive coverage, but those who finance or lease their car will probably find that their lender or lessee requires it. Lenders and lessees are the official owners of the vehicle, so they want to make sure they're adequately protected in case of an incident. For the same reasons, you'll rarely be able to buy comprehensive insurance without also purchasing bodily injury liability and collision coverages.
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Actual cash value equals the purchase price of your car minus depreciation and your deductible. So comprehensive coverage will pay an amount up to the actual cash value of your car to either repair or (in the case of a total loss) replace it. If the cost of repairs exceeds your car's ACV, your car insurance company will declare it a total loss and pay the sum of the car's ACV to help you replace it — unless you opt to retain salvage (i.e., keep the totaled car), in which case the salvage value will also be deducted from your payout.
Let's use the aftermath of Superstorm Sandy as an example to illustrate the differences between collision and comprehensive. Within that storm, let's consider two events that might have happened: 1) a heavy tree branch fell on your car, or 2) you swerved to avoid a falling tree branch and wound up crashing into a tree. In the first event, you had no control over when or why a tree branch would fall on your car. This kind of accident would get reimbursed under your comprehensive policy. In the second situation, you were driving the car and ultimately swerved into the tree, which makes it a collision, and collision insurance therefore pays for the damages. Events like the hypothetical ones stated above are why it's important to differentiate between the two types of coverage.
Comprehensive insurance is a coverage that helps pay to replace or repair your vehicle if it's stolen or damaged in an incident that's not a collision. Comprehensive typically covers damage from fire, vandalism or falling objects (like a tree or hail). If you're financing or leasing your car, your lender likely requires comprehensive coverage. If you own your vehicle outright, it's an optional coverage on your car insurance policy.