What happened to the second VPOTUS? Well he, too, became the POTUS four years later in 1801 after the only Presidential Election pitting the sitting VPOTUS versus the sitting POTUS.
Okay, now there's a little break in the vice presidents going right to the top job. The Secretary of States get the attention for awhile, while the 12th Amendment, separate votes for president and vice president, diminished the quality of men for the poorly created second-in-command of the United States Government. USA! USA! USA! The 3rd VPOTUS, Aaron Burr, after nearly becoming the 3rd POTUS when the 1800 election didn't produce a majority in the Electoral College, but rather a tie. Burr went on to murder Alexander Hamilton in a duel in 1804 which helped to ruin his reputation as well as some treasonous actions in the West.
Burr's successors in the vice presidency, George Clinton, Jefferson's second VPOTUS and Madison's first VPOTUS, and Elbridge Gerry, Madison's second vice president, died in office. The 6th VPOTUS, Daniel D. Tompkins, was only the second vice president to be elected to two terms and serve the full 8 years after John Adams, the 1st VPOTUS. It wouldn't be until 1912, when Thomas R. Marshall was elected the 28th VPOTUS and served two terms and eight years. However, unlike Vice President Adams or even Vice President Jefferson, Vice President Tompkins would not run for the presidency and would end up dying just months after leaving office in 1825.
John C. Calhoun would be safely elected vice president in the crazy, but interesting, 1824 Presidential Election. Calhoun was the vice presidential nominee for both Andrew Jackson and John Quincy Adams. While the presidential race was chaos with four candidates from the same party, since the Federalists were finished as a national political party after the success of the War of 1812. The factions that made up the Democratic-Republicans, had four candidates for the top of the ticket and three for the bottom. While Jackson would win a plurality of both popular votes (not all States votes were counted at this point, but those that were Jackson had the most) and the Electoral College, but not a majority. Calhoun however did receive a majority of Electoral Votes and became the 7th VPOTUS and had to wait to see who his president would be. Vice President Calhoun would be the second and, so far, last vice president to serve two different presidents.
When the House of Representatives elected John Quincy Adams the 6th POTUS, Jackson essentially campaigned against Adams 6 for the next four years. Jackson's supporters, calling themselves Democrats, helped put Jackson in the Executive Mansion in 1829 with Calhoun reelected to a second term, but with a new president. Calhoun would be the last reelected vice president until Vice President Marshall wins with Woodrow Wilson in 1916 for a second term. However, Calhoun would not finish his second term. He would resign the vice presidency in the Presidential Election year of 1832, so he could be elected Senator from South Carolina. He was a thorn in President Jackson's side, probably just as ruckus as the Adams 2/Jefferson administration from 1797-1801.
It is with Vice President Calhoun's successor and President Jackson's second vice president, Martin Van Buren, where the sitting vice president has a chance for the top job. The one term vice president would be elected to one term and kicked out of office thanks to bad economic times.
After Van Buren's jump right from the vice presidency to the presidency, it would be some time before anyone attempted it or do what Adams 2, Jefferson and Van Buren had accomplished. Van Buren's own vice president, Richard M. Johnson, who needed the Senate to be elected vice president since he was a few votes shy of a majority in the Electoral College thanks to his relations with a slave, did not run for the presidency and is part of that great pantheon of unknown 19th Century vice presidents. From 1841 to 1965, there would be vice presidents that become president through death, natural or assassinated, like John Tyler, Millard Fillmore, Andrew Johnson, Chester A. Arthur, Theodore Roosevelt, Calvin Coolidge, Harry S. Truman, and Lyndon B. Johnson. Of that group, Tyler through Arthur never faced the People at the top of the ballot, Fillmore did as a third party candidate in 1856 for the Know-Nothing Party and won Electoral Votes. Not that late 20th Century/early 21st Century third party placing $#!t. The remainder of that list won reelection to the presidency in their own right after serving out the term of the fallen president. The 1860 Presidential Election had the incumbent Vice President John C. Breckinridge, the youngest VPOTUS to serve at 36 in 1857 with President James Buchanan, ran against the GOP's second presidential candidate, Abraham Lincoln and the Democratic Party's Stephen Douglas. While Lincoln came in first in both popular and Electoral Votes, Breckinridge came in second in the Electoral College and third in popular votes after Douglas. Breckinridge of course carried the South, as he ran as the candidate for the Southern Democratic Party. Breckinridge, like all incumbent vice presidents, had to read the winner of the Electoral College during a Joint-Session of Congress, announcing his loss and his opponent's victory. Unlike Vice President Breckinridge, Vice Presidents Adams, Jefferson, and Van Buren announced their victories as Commander-in-Chief.
100 years after Vice President Breckinridge's loss, Vice President Richard M. Nixon would have to announce his defeat in the close 1960 Presidential Election with Senator John F. Kennedy. Nixon was the first incumbent vice president to run for the presidency since Breckinridge. Eight years later in 1968, Hubert Humphrey would follow in Nixon's footsteps as the next eligible incumbent vice president to try for the top of the ticket. Like Nixon's 1960 close election, the incumbent vice president lost in a SUPER close race, this time however Nixon was on the winning side of the election, becoming the first former vice president to win the presidency.
From there the next eligible V.P. would be George Bush in 1988. Nixon's vice president, Spiro Agnew, would resign, becoming the second to do so and be replaced by first-appointed vice president under the 25th Amendment, Gerald Ford. Ford would of course go on to be POTUS, the first to never run for the office or the vice presidency. Jimmy Carter and his running-mate, Walter Mondale, would lose a second term to Ronald Reagan and George Bush in 1980, but as if he served 8 years, Mondale tries his turn at the top of the ticket in 1984 and did worse than when he was on the bottom four years prior. So with Reagan and Bush's reelection in '84 and the 22nd Amendment limiting Reagan to two terms, Bush was next as the incumbent vice president for the top of the Republican Party's ticket in '88.
Bush 41 would be the first sitting vice president to run since Humphrey ran 20 years prior, but unlike the 1968 Democratic Candidate, Bush 41 was more like the Democratic Vice President in 1836, Martin Van Buren, the last incumbent to win the presidency. So for the first time in the 20th Century and since Van Buren in 1837, the vice president of the United States announced his win in the Electoral College making him the next president of the United States. Had Bush 41 won reelection in 1992 (some say he would have had Ross Perot not been in the race, since as a third party candidate Perot siphoned) and served out his second term until 1997, he would've been the first person to have served two terms as vice president and two as POTUS, just it would have been for another presidential father, Adams 2 in 1800. Jefferson served one term as VPOTUS and two as POTUS. MVB served one term as both the VP and POTUS. Nixon has been elected twice to both the presidency and vice presidency, but he did not complete his second term. There's a record to be broken, that's four out of five national elections. The 5th election was the super-close 1960 Presidential Election where JFK defeated the incumbent Vice President Nixon.
Al Gore. Tennessee. 45th VPOTUS. 1993-2001. Democratic. 2000 Democratic Presidential Candidate and winner of the Popular Vote in the 2000 Presidential Election. The screen capture is of his concession speech on December 13, 2000 after 36 days of recounts and legal battles.
Al Gore would come very very close to the presidency with a win in the popular vote in 2000 but not in the Electoral College thanks to the U.S. Supreme Court's ruling in Bush v. Gore, which ended the recounts in Florida which then gave the State's votes to Bush 43. Eight years later in 2008, Vice President Richard Cheney would not run for the presidency. The chances of the current Vice President Joe Biden running in 2016 are slim. He will be 74 and while 74 is the new 64, he faces popular challengers from his own party and the GOP. So only time will tell if a future vice president will be a Bush 41 (winner), a Gore (super close), a Humphrey (close enough), a Mondale (loser, electorally), or a Nixon (all of the above).