Most states do not require serial numbers for motors. There are some places in the world which do, so if you travel and cross international borders, you should have documentation. Generally a bill of sale would have the engine serial numbers. The boat will be registered, titled or documented. The trailer will also be registered or titled. (some states don't title boats and some don't title trailers under a certain size). Be sure that the serial numbers match with the boat and the documentation--same for the trailer. Some states will inspect the boat and trailer to varify the numbers.