Only once: 1797-1801, John Adams and Thomas Jefferson
Beginning in 1804, each Presidential candidate ran as a team with his "running mate" (Vice Presidential candidate).
Yes, there have been instances where an incumbent president has lost the nomination for their party. One notable example is President Franklin Pierce, who failed to secure the Democratic Party's nomination for a second term in 1856.
No- there is no guarantee that the incumbent president will be nominated by his party for another term. Tyler, Fillmore, Pierce and Andrew Johnson all found this fact to be true through personal experience. Lyndon Johnson was so severely challenged for the nomination in 1968 that he decided not to seek another term. Others have been challenged but survived the challenge .
Although the candidates for President are put forward by political Parties, they have no formal role within their Party. They may - because of the prestige of the Presidency - have (even considerable) influence on Party politics and strategy, but there have also been many instances where Presidents' influence on their Party was only very limited. In an ideal world, the President is the person trying to transform his Party's aims into legislation and executive action. In practice, if he faces a hostile Congress with a majority of a rival Party there is only little he can achieve.
Yes, there have been instances in which an incumbent president has chosen not to run for re-election.
Ed Milliband has just been elected leader of the Labour Party. It hasn't got a president.
Each President is party of a political party traditionally it has been either the Republican or Democratic parties. The party that the President is aligned with will determine the type of agenda the President pushed either a conservative or liberal agenda.
A democratic party, as you have been voted to power by fair means.
It was the first president elected from an opposition party. For 1929 to 2000 presidents have been from the party PRI.
In 1860, former Whig Party members of the South who did not agree with the platforms of the Republican Party, the Northern Democratic Party, nor the Southern Democratic Party formed the Constitutional Union Party, which adopted the slogan "the Union as it is, and the Constitution as it is." At their National Convention, on the second ballot, they selected as their presidential nominee U.S. Senator from Tennessee John Bell over Texas Governor and former Texas President Sam Houston. (If Houston had won the nomination, he would have been the only presidential candidate in U.S. history who had been President of another country.)
President Obama is a Democrat. He has always been affiliated with the Democratic party.
Hubert h. Humphrey
Herbert Hoover. He was the president of The People's Republic of Quebec before it was annexed by Canada