Let’s start off with the 14 Presidents who served as Vice President:
•John Adams (1789-1797 under President Washington)
•Thomas Jefferson (1797-1801 under President Adams)
•Martin Van Buren (1833-1837 under President Jackson)
•John Tyler (1841 under President Harrison)
•Millard Fillmore (1849-1850 under President Taylor)
•Andrew Johnson (1865 under President Lincoln)
•Chester Arthur (1881 under President Garfield)
•Theodore Roosevelt (1901 under President McKinley)
•Calvin Coolidge (1921-1923 under President Harding)
•Harry Truman (1945 under President Roosevelt)
•Lyndon Johnson (1961-1963 under President Kennedy)
•Richard Nixon (1953-1961 under President Eisenhower)
•Gerald Ford (1973-1974 under President Nixon)
•George H.W. Bush (1981-1989 under President Reagan)
Eight of those Vice Presidents succeeded to the White House upon the death of a President; Ford became President upon Nixon’s resignation; and five were elected on their own: Adams, Jefferson, Van Buren, Nixon, and Bush.
As for other high-level positions in the Cabinet or line of succession:
Thomas Jefferson
•Secretary of State (1790-1793 under President Washington)
James Madison
•Secretary of State (1801-1809 under President Jefferson)
James Monroe
•Secretary of State (1811-1817 under President Madison)
•Secretary of War (1814-1815 under President Madison)
[Monroe held both Cabinet positions simultaneously]
John Quincy Adams
•Secretary of State (1817-1825 under President Monroe)
Martin Van Buren
•Secretary of State (1829-1831 under President Jackson)
James Buchanan
•Secretary of State (1845-1849 under President Polk)
William Howard Taft
•Secretary of War (1904-1908 under President Roosevelt)
•Acting Secretary of State (1905 during the illness of John Hay)
•Chief Justice of the United States Supreme Court (1921-1930, appointed by President Harding; not a Cabinet-level position or in the line of succession, but the only President to lead the Judicial branch)
Herbert Hoover
•Secretary of Commerce (1921-1928 under President Harding and President Coolidge)
George H.W. Bush
•United States Ambassador to the United Nations (1971-1973, appointed by President Nixon; the position of U.N. Ambassador wasn’t a Cabinet-level office at the time)
•Director of the CIA (1976-1977, appointed by President Ford; not a Cabinet-level position or in the line of succession, but powerful nonetheless)