John Tyler became the first vice president to become president after William Henry Harrison died 30 days after being inaugurated. The U.S. Constitution didn't clearly state that the vice president officially became the president until the passage of the 25th Amendment in 1967. Tyler, in 1841, established the precedent which Millard Fillmore, Andrew Johnson, Chester Arthur, Roosevelt 26, Calvin Coolidge, Harry Truman, and LBJ would all follow until the amendment was written. But it wouldn't be until Roosevelt 26 in 1904, that one of these VPOTUS turned POTUS would win an election after succeeding to the office. Some would try to run for the job they got from outside the democratic process (although elected vice president), but only a few would actually get the chance to try on their own...and even win.
For Tyler, he was more of an independent after being shunned by the Whig Party that nominated him as vice president in 1840 and the Democrats didn't want him. He considered running as an independent but chose not to run in the end. Fillmore, Johnson 17, and Arthur weren't even given a chance for renomination. Tyler would eventually side with the Confederate States of America, or as Lincoln called them the States in rebellion, or something like that. Fillmore gave the presidency another chance in 1856 as the Know Nothing Party's presidential candidate. He would place 3rd in the general election and not like early 21st Century 3rd Parties and their 3rd place positions. Fillmore would win a State, Maryland and not his home State of New York, which means 8 electoral votes and 21% of the popular vote. Johnson 17 would get reelected to the U.S. Senate from Tennessee becoming the first and only former president to be elected to the Congress as a senator, but never ran at the top of a presidential ticket. Arthur wanted to try but realized, like Fillmore in 1852, the party wasn't with the incumbent. A challenge TR wouldn't have to face thus starting a new trend.
TR was a popular American with his stories of gallantry in the Spanish-American War leading the Rough Riders. He'd served as McKinley's Assistant Secretary of the Navy and went on to be the governor of New York, a stepping stone to national office. When McKinley's first vice president, Garret Hobart, died in 1899, Roosevelt was put on the ticket because New York Republican Party bosses wanted to put an end to TR's corrupt-busting from the State capital. Of course putting TR, a crazy cowboy according to Mark Hana, McKinley's political brain or Karl Rove, thought it was unwise to put him so close to the presidency. His fears came true when McKinley was shot in September 1901 by Leon Czolgosz. Since McKinley was shot in the first year of his second term, President Theodore Roosevelt's popularity continued to grow through the remainder of that term. His 1904 reelection was a given. However after winning the 1904 election, he declared he wouldn't run for reelection in 1908 because he was following in the tradition set by George Washington and limiting one's self to two terms. Roosevelt 26 considered McKinley's second term as his first term but his declaration as a two term president made him a lame duck president from the start of his second term.
He would however handpick his successor William Howard Taft, his Secretary of War. After realizing Taft was no TR, former President Roosevelt decided to do what only a few former presidents had tried... run for reelection as a former president. Only one has been successful, TR's fellow New Yorker Grover Cleveland. And he was renominated by his own party 3 times in a row. Roosevelt 26 would have to do what former presidents Fillmore and Martin Van Buren did. They went the 3 party route. Whereas Fillmore won a State in 1856, Free Soil Party nominee Van Buren got 10% of the popular vote and no electoral votes. Very modern. All 3 were vice presidents, but Van Buren was the last incumbent vice president to become president through election until 1988 with Vice President George Bush's election to the presidency. As a 3rd Party candidate in 1912, Progressive Party or the Bull Moose Party nominee former President Theodore Roosevelt became the last 3rd Party candidate to come in second place. The 1920 election would be the first election since Roosevelt 26's death in 1919, but there would be a Roosevelt on the ticket. Franklin D. Roosevelt, President Woodrow Wilson's Assistant Secretary of the Navy and future governor of New York, was the Democratic Party's vice presidential nominee to James Cox. A son of Ohio would've been president had either ticket won, but the vice presidents were different. FDR was from New York and Republican vice presidential nominee Calvin Coolidge of Vermont was from Massachusetts. He would be president of the United States before the presidential election of 1924, not that much different from TR 20 years prior.
Calvin Coolidge finished Warren G. Harding's first term after he died of natural causes in 1923. (Myth will have you believe his wife, Florence Harding, poisoned President Harding...she didn't. But there are some that would want you to think that.) Coolidge presided over a prosperous America in the Roaring 20s and was easily renominated by the GOP in 1924. Like Roosevelt 26, but not with the proclamation of not running in 1908 (which limited TR from seeking his own second term or historically speaking an unheard of 3rd term), Coolidge didn't run for another term in 1928 in the days before the 22nd Amendment which limited presidents to two terms, or 8-10 years in office. But Coolidge's successor, Herbert Hoover would face the man in 1932 for which the 22nd Amendment was passed, Coolidge's rival for the vice presidency 12 years before.
Franklin D. Roosevelt was the first and only man to be elected to a third and fourth term. He also had the most vice presidents, 3. And it was lucky number 3 that succeeded him after he passed in April of 1945. Harry Truman was the lucky one of FDR's vice presidents and served about two and a half months as the nation's number 2 before taking on the big job of filling the shoe's of the POTUS that presided over the nation through the Great Depression and most of the Second World War. Truman's chances of reelection weren't great by 1948, but at least he was easily renominated. The election was close and even though everyone including the press thought Thomas E. Dewey, Governor of New York (there's that State again) and 1944 Republican Presidential Nominee, would be the 34th POTUS. Truman woke up to learn that he had finally become a president-elect.
Like Johnson 17, Arthur and Roosevelt 26's ascensions to the presidency, LBJ, or Johnson 36, would also become president because of an assassin. John F. Kennedy was killed in Dallas, Texas, on November 22, 1963, while riding in the backseat of an open motorcade. Johnson 36 was sworn in on Air Force One before taking off for Washington, D.C. In 1964, LBJ's popularity propelled him into his own term as president with one of the biggest landslides in a presidential election.
It would be during Johnson 36's term that the 25th Amendment would pass and put John Tyler's precedent into the Constitution. "In case of the removal of the President from office or of his death or resignation, the Vice President shall become President.". It also makes sure there is no vacancy in the vice presidency. When all the vice presidents listed above became POTUS, the office of the vice president remained vacant, as well as the times that the vice president died while in office. Vice President James Sherman was the last to die in office just weeks before the 1912 election. Votes for Sherman would go to Nicholas Butler of New York. This amendment takes care of that.
So when Spiro Agnew became the second vice president (after John C. Calhoun in 1832) to resign from the office in 1973, Richard Nixon became the first POTUS to use the 25th Amendment and fill the vacancy. Gerald Ford became the first vice president never elected by the people, but approved by a majority of the Congress of the United States, House and Senate. With Nixon's unprecedented resignation in 1974, Ford was the first unelected POTUS and went on to appoint Nelson Rockefeller as vice president. They would be the first unelected administration. Ford would earn his party's nomination in 1976, even though he did have a challenge from California's Ronald Reagan. But in a close election, Ford would become the first of these 20th Century vice presidents that moved on up to the presidency through death or resignation to lose election to his own term. Unlike his 19th Century vice president-turned-president counterparts, he at least won his party's nomination and got to face the electorate at the top of the ticket.
Nixon's resignation was the last time a vice president, Ford, became president outside of being elected, George H. W. Bush ran for president in 1988 while he served as Reagan's vice president and won. So while 17 won reelection to a second term and 4 won reelection to the presidency, 21 have spent more than four years as president of the United States.