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.
Twenty-second Amendment to the United States Constitution
Theodore Roosevelt succeeded to the presidency on September 14, 1901, following William McKinley's assassination ( days into his second term), and was subsequently elected to a full term in 1904. While he declined to seek a third (second full) term in 1908, Roosevelt did seek one four years later, in the election of 1912, where he lost to Woodrow Wilson. Wilson himself, despite his ill health following a serious stroke, aspired to a third term. Many of Wilson's advisers tried to convince him that his health precluded another campaign, but Wilson nonetheless asked that his name be placed in nomination for the presidency at the 1920 Democratic National Convention. Democratic Party leaders were unwilling to support Wilson, however, and the nomination eventually went to James M. Cox. Wilson again contemplated running for a (nonconsecutive) third term in 1924, devising a strategy for his comeback, but again lacked any support; he died in February of that year.