The other driver's insurance company has declared my car a total loss because of an accident. Is the insurance company required to pay me its replacement cost?
No. The insurance company only has to pay you the fair market value of your car at the time of the accident. The fair market value of your car is what you could have reasonably expected to sell it for in your community. If you paid more for your car than it was worth, or if you owed more on your car than it was worth, you may lose money.
Even if it is a total loss, your car may still have salvage value. If you choose to keep your car, the insurance company can deduct its salvage value from the amount they pay you for your car.