Obviously many US presidential candidates have run in numerous elections, mostly on the tickets of minor parties.

However, I assume you are referring to the major parties. In modern history it is quite common for individuals to lose in the primaries for the nomination (as Clinton did in 2008) and to subsequently run in another election down the line and some of these people have gone onto win a general election. This includes Ronald Reagan (after losing the 1976 Republican nomination to Gerald Ford), George H.W. Bush (who lost the nomination to Reagan in 1980) and a lot of others in earlier periods.

If you are asking "has a person ever been the head of the ticket for a major party, lost a general election, and then been nominated again in a future election and won", then the answer is yes. Richard Nixon did this by winning the 1968 election despite losing in 1960 election to JFK. There are other instances of similar things happening in the 19th century, e.g. in 1836 William Henry Harrison lost to Martin Van Buren and then in 1840 Harrison defeated Buren.

Probably the most famous "Serial Candidate" has to be William Jennings Bryan. His staunchly populist policies and positions, such as opposition to the Gold Standard, carried him to being the Democratic nominee in 1896, 1900, and 1908. He never won but was eventually named as Wilson's Secretary of State. He resigned however over disagreements with Wilson's policies, which he saw as favoring the Entente and dragging America into WW1.

He is also probably most famous for bringing his renowned oratory skills to the Scopes Monkey Trial. There he argued in support of the prosecution of a school teacher who had violated Tennessee law by teach Darwinism.

For the 20th and 21st century, more or less in reverse order:

Mitt Romney sought the Republican nomination unsuccessfully in 2008, and successfully in 2012, but was beaten by Barack Obama in the general election.

John McCain sought the Republican nomination unsuccessfully in 2000, and successfully in 2008, but was beaten by Barack Obama in the general election.

Joe Biden sought the Democratic nomination unsuccessfully in 1988 and 2008, but was nominated and elected Vice President in 2008 and 2012.

Al Gore sought the Democratic nomination unsuccessfully in 1988, was nominated and elected Vice President in 1992 and 1996, was nominated for President in 2000 but beaten by George W. Bush.

Bob Dole was nominated as the Republican candidate for Vice President in 1976, but was defeated along with his running mate Jerry Ford. He sought the nomination unsuccessfully in 1988. He sought the nomination again in 1996, was nominated, but was beaten by Bill Clinton that November.

George H.W. Bush sought the Republican nomination unsuccessfully in 1980, was nominated and elected Vice President in 1980 and 1984, sought and won the nomination in 1988, and was elected President that year, failing of re-election in 1992.

Ronald Reagan sought the Republican nomination unsuccessfully in 1968 (losing to Nixon) and 1972 (losing to Ford), but was nominated and elected in 1980, and re-nominated and re-elected in 1984.

Hubert Humphrey sought the Democratic nomination unsuccessfully in 1952 and 1960, was nominated and elected Vice President in 1964, was nominated for President but lost to Richard Nixon in the general in 1968, and sought the nomination unsuccessfully in 1972.

Richard Nixon was nominated and elected Republican candidate for Vice President in 1952 and 1956, nominated for President in 1960 but defeated by John Kennedy, and nominated for and elected President in 1968 and 1972. Between his first and second Presidential nominations, he was nominated but defeated in the general election for Governor of California, making his comeback that much more impressive.

Lyndon Johnson sought the Democratic nomination in 1960, but was instead nominated and elected Vice President, was nominated and elected President in 1964 (after having taken the office by succession after Kennedy's assassination), sought the nomination again in 1968 but dropped out early in the race in favor of Hubert Humphrey when (lack of) support for Johnson became clear.

John Kennedy unsuccessfully sought the Democratic nomination for Vice President in 1956 when, in a never-to-be-repeated experiment, Adlai Stevenson decided not choose a running mate but make it a free choice of the National Convention delegates. He went on to win the nomination and Presidency in 1960.

As noted above, Adlai Stevenson was nominated by the Democrats in 1952 and 1956, both times losing to Dwight Eisenhower, and failed to win the nomination in 1960 on his third attempt.

Thomas Dewey sought the Republican nomination in 1940 unsuccessfully, and won it in 1944 and 1948, losing to Franklin Roosevelt and Harry Truman, respectively, in the general elections.

Franklin Roosevelt was the Democratic nominee for Vice President in 1920, losing the general election, and nominated and elected President in each of 1932, 1936, 1940 and 1944.

Theodore Roosevelt was the Republican nominee for Vice President in 1900, and President in 1904, winning each time, and then ran unsuccessfully for President as an independent in 1912 after failing to take the Republican nomination from Howard Taft. (TR is by far the most successful third party candidate for President since the modern two-party system arose after Reconstruction.)

The ultimate story of a presidential candidate who was perhaps one of the most capable presidents yet never got elected is the story of Henry Clay.

Henry was one of the great compromisers in the United States; he created the American System (A three piece system that suggested implementing taxes, building a strong banking system, and the establishment of the Erie Canal), the Missouri Compromise (a piece of legislation used to handle slavery/anti-slavery disputes for decades), and the compromise of 1850 (Held the north and south from brink of war). Despite his brilliance, however, his name was blackened after the election of 1824.

In the election of 1824 Clay came in fourth (though William Crawford in third place died shortly after). As speaker of the house he had control over much of the house and since the votes were so close (between Andrew Jackson and John Quincy Adams) the decision was given to congress on who to elect. Jackson was the proposed winner, but John Quincy Adams promised Clay a position in his cabinet if he let him win so Clay gave a speech in congress that flipped the election towards Adams. This would make a large majority of the populous hate Clay.

In the election of 1832 Clay had a decent chance at the presidency but another party was formed that split the votes for his party.

In the election of 1836 Clay ran initially but was utterly ignored as a Whig party candidate in favor of William Henry Harrison.

In the election of 1844 Henry was favored to win, but lost the election due to his indecisiveness as to whether or nor he'd annex Texas as a free/slave state or postpone that problem to a later date. His inability to make a decision had an incredibly negative effect on his election, however, as the Liberty Party (an anti-slavery party in New York) flipped their votes from Henry Clay to James Polk, changing the majority of votes in New York to his rival. James Polk would ascend to the presidency. Henry Clay lost that election by roughly 16,000 votes.

In his final election of 1848 Henry Clay narrowly missed being elected the Whig party candidate, and despite his capabilities was not even suggested as a potential Vice Presidential candidate.

TLDR; Henry Clay was a brilliant legislator and politician who was a 5 time unsuccessful presidential candidate due to corruption and unfortunate circumstances.

Adlai Stevenson was nominated twice by the Democrats to run against Dwight Eisenhower.

Neither election was especially close: partly, of course, because of Ike's popularity, and partly because of Stevenson's reputation as an intellectual, with a demeanor to match. It is worth noting that the term "egghead" has only two citations in the OED before 1952 (one in a private letter by Carl Sandburg that somebody must have worked really hard to dig up) and seven in the decade of the 50s alone. We can justifiably thank Adlai Stevenson for that contribution to our language, even if it wasn't his intention.