This depends on what time period of American history you are asking about. In pre-Revolution America, the frontier was set by the British under the Proclamation Line of 1763, which forbade colonists from settling west of the Appalachian mountains. The proclamation line was later adjusted to stretch out further west into modern day Kentucky & West Virginia, stopping at the Ohio River. The Northwest Ordinances of 1787, passed under the Articles of Confederation government (one of its few accomplishments) pushed the frontier into the Ohio River Valley.

You can actually use a neat little tool provided by the Census Bureau here to visualize how the frontier line moved further and further west with each passing decade. The completion of the first transcontinental railroad in the 1860s marked the beginning of the end for the American frontier. Spurs off of this route allowed pioneers to reach even deeper into areas of the continent that had yet to be settled. After the 1890 census, the U.S. government concluded that there was no longer a "frontier line of settlement".

You could say that actual Wild West lasted a bit longer than the frontier line. Most mark the end of this era with the admission of Arizona to the union in 1912, and the invention of cheap consumer automobiles shortly after.