The ideals of the American Revolution were (according to some) brought back with the French army to France, where the French Revolution of 1789 broke out.
However, unlike the American Revolution, the French weren't a colony, they couldn't just stop taking orders from the King. They had a massive armed revolt against him; peasants and the poor rose up against the aristocracy, the King and other aristocrats were executed by the "will of the people". The French revolution was supposed to be the beginning of a "liberalization" movement across Europe. However the Kings and Princes of France's neighbors helped to militarize the new state (even more), the ideas of liberty began to be secondary to the needs of security in the new embryonic state. From this point onwards there was massive upheaval in Europe, wars were fought on Ideological, rather than dynastic terms.
American colonists offered Washington a crown to be King of the colonies, he refused, and wanted a republic formed.
In France the military gained power and influence, and Napoleon crowned himself Emperor, showing how (as in many revolutions) the revolutionaries often revert to the same types of society as the ones that preceded them. The significance to other nations, I suppose you could say the American Revolution was one of the few revolutions where the principles of the revolutionaries were put into place, without a fall into authoritarianism or despotism. The fact that the colonies were thousands of miles away from any potential enemies meant that the American revolutionaries never had to face multiple counter-revolutionary assaults after the original success.
Liberty, republicanism, and independence are powerful causes. The patriots tenaciously asserted American rights and brought the Revolution. The Revolution brought myriad consequences to the American social fabric. There was no reign of terror as in the French Revolution. There was no replacement of the ruling