Who was the only president to be elected president and vice president?

This has happened to more than one man, in fact several men have been elected to both offices:

John Adams (1st Vice President, 2nd President)

Thomas Jefferson (2nd Vice President, 3nd President)

Martin Van Buren (8th Vice President, 8th President)

Theodore Roosevelt (25th Vice President, 26th President) *succeeded McKinley

Calvin Coolidge (29th Vice President, 30th President) *succeeded Harding

Harry Truman (34th Vice President, 33rd President) * succeeded FDR

Richard Nixon (36th Vice President, 37th President)

Lyndon B. Johnson (2nd Vice President, 3nd President) *succeeded Kennedy

George H.W. Bush (43rd Vice President, 41st President)

There is not "only one". George Bush (the first one), Richard Nixon, Lyndon Johnson, Harry Truman, Calvin Coolidge, Theodore Roosevelt, Martin Van Buren, Thomas Jefferson, and John Adams were all elected as both President and Vice President. (Though in the case of Jefferson and Adams, under the Constitutionally-prescribed rules for choosing Presidents and Vice Presidents at that time, they were "elected" Vice President only because they came in second in the Electoral College vote for President - Adams second to Washington, twice, and Jefferson second to Adams - before succeeding in a subsequent election. This is not so much "being elected Vice President" as it is "losing the election for President."

Perhaps you meant to ask who was the only President who was NOT elected as either President or Vice President. That would be Gerald Ford, appointed as Nixon's Vice President in 1973, and succeeded to the Presidency in 1974.