Below is an unofficial list, using either the Constitution or the appropriate supporting federal law (the Presidential Succession Acts of 1792, 1886 or 1947, as the case may be), of Presidents of the United States together with the person next in the line of succession, when each assumed that role, and the office that they held which placed them next in line.  The list is based on information retrieved from public sources, so while it is by and large accurate, some errors may exist.

In cases where a number in parenthesis appears next to a name or office, supplementary information is provided after the list below.

Notes regarding the above list:

1. Died in office.
2. Resigned from office.
3. See "1849:  President Who?" for more information.
4. When MILLARD FILLMORE ascended to the presidency, there was no sitting President Pro Tempore of the Senate, and Howell Cobb, who served as Speaker of the House of Representatives, was constitutionally ineligible to act as President.
5. Second time in office or "next in line," as the case may be.
6. On January 19, 1886, President GROVER CLEVELAND signed the Presidential Succession Act of 1886 into law, which changed the order of succession so that the Secretary of State was "next in line" should there be no Vice President.
7. On January 18, 1947, HARRY S TRUMAN signed the Presidential Succession Act of 1947 into law, which changed the order of succession so that the Speaker of the House of Representatives was "next in line" should there be no Vice President.
8. Third time in office or "next in line," as the case may be.

Other things worth noting:

1. For purposes of the list above, Presidents resuming the powers and duties of their offices following an invocation of the 25th Amendment are not considered to have served non-consecutive terms.  However, for purposes of being "next in line" above, Vice Presidents completing such service as Acting President are.
2. JOHN ADAMS was sworn in as the nation's first Vice President on April 21, 1789, nine days before George Washington was sworn in as President.  While some may consider him to be a de facto Acting President during this period, as there was neither a succession law in place nor an office of President to succeed to, such claims are specious at best.
3. WILLIAM RUFUS DeVANE KING was the first person to be "next in line" on two separate occasions.
4. WILLIAM RUFUS DeVANE KING, SCHUYLER COLFAX, and THOMAS FRANCIS BAYARD each hold the distinction of being "next in line" on multiple occasions, but by virtue of holding different offices in each case.
5. RICHARD BRUCE CHENEY is the only person to have been "next in line" on three distinct occasions, having been called upon to act as President briefly twice during the administration of GEORGE WALKER BUSH.