Roman laws were adopted and modified by the various European kingdoms even after the fall of Rome. These laws (through the legal systems of the first colonies) were passed on to the fledgling USA. The rule "Let the buyer beware" AKA caveat emptor is from the old Roman law meaning the buyer is at fault if there is a problem with a product they purchased. It is still the basis for most consumer law in the USA, although it has been modified to an extent due to people like Ralph Nader.
The Romans had a reperesentative form of government, in which officals were elected to represent larger groups of voters, a system that is used in the USA.