George Washington
At the end of his second term, Washington retired for personal and political reasons, fatigued and disgusted with personal attacks, and to assure a truly contested presidential election could be held. He did not feel bound to a two-term limit, but his retirement ultimately set precedent. The two-term limit to the presidency was formalized with the 1951 adoption of the Twenty-second Amendment to the United States Constitution. Washington is often credited with setting the principal of a two-term presidency, but it was Thomas Jefferson who first refused to run for a third term on political grounds.
Term limits in the United States
Thomas Jefferson mentioned that Washington retired after serving only two terms, without mentioning that Washington opposed the policy Jefferson was proposing. Crockett argues that Washington "did not intentionally establish the so-called two-term tradition; his departure was motivated by a desire to demonstrate that the country could function without him and to retire to Mount Vernon. He made no principled argument for limiting presidents to two terms, and in fact disagreed with Thomas Jefferson on this point." The "two term tradition" was created in 1807-1808 and it is often mistakenly suggested Washington had launched the policy. 
In 1861, the Confederate States of America adopted a six-year term for their president and vice-president and barred the president from seeking re-election. That innovation was endorsed by many American politicians after the Civil War, most notably by Rutherford B. Hayes in his inaugural address. Ulysses Grant was urged to run for a third term in 1876, but he refused. He did try to win the 1880 nomination, but was defeated in part because of anti-third-term sentiment. Theodore Roosevelt had already served over 7 years and in 1912, after a four-year hiatus, ran for a third term. He was violently criticized; indeed, he was almost killed by John Flammang Schrank, who was obsessed with stopping a third term.