Twenty-second Amendment to the United States Constitution
Some argue that the 22nd Amendment and 12th Amendment bar any two-term president from later serving as vice president as well as from succeeding to the presidency from any point in the presidential line of succession. Others contend that the original intent of the 12th Amendment concerns qualification for "service" (age, residence, and citizenship), while the 22nd Amendment, concerns qualifications for "election", and thus (strictly applying the text) a former two-term president is still eligible to "serve" as vice president (neither amendment restricts the number of times an individual can be elected to the vice presidency), and then succeed to the presidency to serve out the balance of the term (though prohibited from running for election to an additional term).
George Allen (American politician)
Barred by term limits from seeking reelection to a second term in 1997, he worked in the private sector until the 2000 election in which he ran for the United States Senate, defeating two-term Democratic incumbent Chuck Robb. Allen ran for reelection in the 2006 election, but after a close and controversial race, he was defeated by Democratic former U.S. Secretary of the Navy Jim Webb. When Webb decided to retire, Allen ran for his old seat again in the 2012 election but was defeated again, this time by Democratic former Governor Tim Kaine. Allen now serves on the Reagan Ranch Board of Governors of Young America's Foundation, where he is a Reagan Ranch Presidential Scholar.