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).
President of the Philippines
Article 7, Section 2 of the Constitution reads:
"No person may be elected President unless he is a natural-born citizen of the Philippines, a registered voter, able to read and write, at least forty years of age on the day of the election, and a resident of the Philippines for at least ten years immediately preceding such election." 
The Constitution also provides term limits where the President is ineligible for reelection and a person who has succeeded as President and has served as such for more than four years will be ineligible to be elected for a second term. However, with the case of Joseph Estrada who was elected president in 1998, deposed in 2001, and again ran for the presidency in 2010, the Constitution's wording where "[the] President shall not be eligible for any re-election" remains unclear as his case was never brought to the Supreme Court. It remains unclear whether the term limit of no re-election applies only to the incumbent President or for any person who has been elected as President.