Usually, state laws have to be followed, but generally, if a car is totaled by adjuster, there are a few options. Most people will just take the payout from their insurance company and let them handle it. However, you could get a salvage title and attempt to sell it on your own to either a dealership or a private party. Keep in mind the salvage certificate will stay with the car as long as the car is around. This means most warranties will be voided, as well there will be higher insurance costs, so it's not always the easiest transaction to complete. If these avenues don't work, you can always sell it to a junkyard or donate it for a tax credit.
Before you start shopping, understand how to compare car insurance.