The American Revolution (also called the American Revolutionary War) was a series of events and military conflicts that took place in North America from 1774 until 1783, through which the thirteen colonies of the United Kingdom of Great Britain on the continent gained their independence, and formed the United States of America.
During the Battle at Valcour Island on 11 October 1776, the Continental Navy sloop-of-war Enterprise under the command of Israel Daniel Dickenson evaded a fleet of British warships in Lake Champlain and denied Britain a decisive victory. Subsequent events stalled British activity until next spring, giving America time to fortify defenses. (ST - Enterprise Logs short story: "The Veil at Valcour")
During his encounter with Doctor Beverly Crusher, terrorist leader Kyril Finn compared himself to American General George Washington in his struggle to gain independence from the Rutians for the Ansatan people. Crusher rejected the comparison, stating that Washington did not target innocent civilians. (TNG episode: "The High Ground")
A mid 24th century monograph by Montmorency entitled Benedict Arnold, Patriot, made the case that the infamous American traitor Benedict Arnold was in fact a double agent who undermined British military efforts in America. This interpretation was generally accepted as the final authority on Arnold by the 2360s. (TNG comic: "The Lesson")
During the Dominion War, Captain Benjamin Sisko compared the situation faced by the United Federation of Planets and its allies to the American's situation at Valley Forge in the winter of 1777-78, when they seemed to be on the verge of defeat, and yet went on to victory. (DS9 novelization: Call to Arms...)