The rule of law: The American political system is based on the idea that government is a government of laws, not men. In other words, government operates according to the rule of law, not the arbitrary whims of individuals. Among other things, this means that power must only be exercised according to the law.
It's somewhat ironic that this is an idea inherited from the British political system, as the American colonists believed that the British government had departed from the rule of law in administering their colonies. To some extent, the American Revolution was an attempt to reclaim a principle of governance which had been tainted by the actions of successive British governments.
A legal system based on common law: With the notable exception of Louisiana, every state's legal system is based on common law. This is essentially a judge-made law handed down from case to case by way of judicial precedent. It is an inheritance from the English system of common law, which goes back several hundred years and was seen, in a limited respect, as placing a limit on government power.
A tradition of liberty: Many of the Founding Fathers were strongly influenced by the Magna Carta, a document that sought to protect ancient liberties from an over-mighty king. By the time of the American Revolution, however, it seemed to many in the colonies that the British were turning their back on this venerable tradition by exercising tyrannical governance. In breaking free from the British and setting up their own institutions of government, the Founding Fathers were, to some extent, attempting to revitalize the lost tradition of English liberty enshrined in the Magna Carta.