Presidential Line of Succession

Also, if the would-be successor does not meet the constitutional requirements for President then the presidency would skip them and go to the next person in the list.

1) Vice President

2) Speaker of the House of Representatives

3) President Pro Tempore of the Senate

4) Secretary of State

5) Secretary of the Treasury

6) Secretary of Defense

7) Attorney General (aka: Secretary of Justice)

8) Secretary of the Interior

9) Secretary of Agriculture

10) Secretary of Commerce

11) Secretary of Labor

12) Secretary of Health and Human Services

13) Secretary of Housing and Urban Development

14) Secretary of Transportation

15) Secretary of Energy

16) Secretary of Education

17) Secretary of Veteran Affairs (thanks CentrX and narzos)

18) Secretary of Homeland Security

It is important to note that whenever one of these people ascends to the Presidency through the Succession Act, he immediately fills all vacant positions in this order with new appointees. So, in order for say, the Secretary of Labor to become president, all 10 people before him have to die all at once (or at least, before they can appoint new officers for the vacant positions). Repeated deaths of only the President would just involve the Vice President assuming office, and appointing a new Vice President, who would then assume office on his death, ad nauseam.