If you have a right to collect for any repairs that need to be done to your damaged vehicle (your auto insurance policy will outline your coverages, deductibles, etc.), the auto insurance company is required to do a visual evaluation of damages so they can begin the process of determining the cost of repairs. Again, a quick look at your insurance policy will tell you exactly what is covered. Based on the damages and what is covered under your policy, the adjuster will provide a reasonable car accident estimate. The auto insurance company is not legally obligated to accept a higher estimate.
The best thing you can do if you have been involved in a collision is to participate in the evaluation and fully cooperate. It is perfectly fine to accompany the claims adjuster while he inspects your vehicle. It is important to point out any damage that the claims adjuster might miss, but keep in mind that extensive damage to your vehicle may result in a "total loss." A total loss is a loss of sufficient size such that there is nothing left of value. This term is also used to mean a loss requiring the maximum amount a policy will pay.
If your car is declared a total loss, the auto insurance company is under no obligation to repair the damages, no matter how much you love your vehicle. What they are obligated to do is, offer you a check for the fair market value of the vehicle. Fair market value is based on what the car would sell for under current market conditions, before the accident.
In the end, it might cost less money to pay the lower estimate now than to drag your feet and wind up in court. A judgment rendered against you can result in court costs in addition to damages and attachment of your wages and bank accounts. Not only can this hurt financially, it can harm your reputation with your bank and your employer.