Chester A. Arthur
If President George W. Bush left the White House or was assassinated or died, his position would e taken over by the Vice President, in this case, Dick Cheney.
President Kennedy had been assassinated.
Spiro Agnew in 1973. He was the second to resign.
Abraham Lincoln was assassinated while he was president and did not have a chance to take any other occupations.
The Speaker of the House and then the president pro tempore of the Senate would take over in a catastrophic event that wiped the president and VP together.
The first vice president to take over office was John Tyler.
John Tyler was the first to take over for an elected president.
Speaker of The House
If you are asking what would happen if a president were to die in office, this has happened to several presidents, including John F. Kennedy (who was assassinated) and Warren G. Harding (who died from a lingering illness); in the case that a president dies during his term, his vice president would take over for him, which is what happened when Harding died suddenly in 1923: his vice president, Calvin Coolidge became president; and when Kennedy died in 1963, his vice president, Lyndon Johnson, assumed the presidency. So if something were to happen to President Obama, his vice president Joe Biden would take over.
The Vice President.
When Lincoln was assassinated, Vice President Andrew Johnson became the new President. No new Vice President was chosen; the office was vacant until Ulysses Grant was elected President in 1868 and Schuyler Colfax became Vice President. This is why the Constitution was amended in 1967, with the 25th Amendment. It finally set rules for how a new Vice President is chosen when the sitting Vice President has to take over the Presidency.
President Kennedy had been assassinated and a transfer of power was necessary.