Going through the list:
George Washington: General, colonial legislature, Continental Congress
John Adams: Colonial legislature, Continental Congress, ambassador, Vice President
Thomas Jefferson: Colonial and state legislature, Continental Congress, ambassador, Governor, Secretary of State, Vice President
James Madison: Continental Congress, House of Representatives, Secretary of State
James Monroe: Colonial legislature, Continental Congress, Senator, Governor, ambassador, Secretary of State, Secretary of War
John Quincy Adams: Ambassador, Senator, Secretary of State
Andrew Jackson: General, House of Representatives, Senator, judge
Martin Van Buren: State legislature, Senator, Governor (he only served as Governor for two months before resigning to become Secretary of State), Secretary of State, Vice President
William Harrison: General, state legislature, House of Representatives, Senator, Territorial Governor, ambassador
John Tyler: State legislature, House of Representatives, Governor, Senator, Vice President (became President after Harrison’s death)
James Polk: State legislature, Speaker of the House of Representatives, Governor
Zachary Taylor: General (had never held any political office before the Presidency)
Millard Fillmore: House of Representatives, Vice President (became President after Taylor’s death)
Franklin Pierce: House of Representatives, Senator, general
James Buchanan: House of Representatives, Senator, ambassador, Secretary of State (he was the last Secretary of State to be subsequently elected President)
Abraham Lincoln: four terms in the Illinois House of Representatives, one term in the U.S. House of Representatives
Andrew Johnson: State legislature, House of Representatives, Governor, Senator, Vice President (became President after Lincoln’s death)
Ulysses Grant: General (had never held any political office before the Presidency)
Rutherford Hayes: General, House of Representatives, Governor
James Garfield: State legislature, General, House of Representatives (the only serving member of the House of Representatives to be elected President)
Chester Arthur: General (served in the Quartermasters Corps and did not serve in battle), Collector of the Port of New York, Vice President (became President after Garfield’s death)
Grover Cleveland: Sheriff of Erie County (1871-1873), Mayor of Buffalo (1882-1883), Governor of New York (1883-1984) (he resigned the office of Mayor to become Governor and resigned the office of Governor to become President)
Benjamin Harrison: General, Senator
William McKinley: House of Representatives, Governor
Theodore Roosevelt: State legislature, NYPD Commissioner, Assistant Secretary of the Navy, Governor, Vice President (became President after McKinley’s death)
William Taft: Solicitor General, federal judge, territorial governor, Secretary of War
Woodrow Wilson: Governor of New Jersey (1911-1913) (resigned to become President)
Warren Harding: State legislature (1899–1903), Lieutenant Governor of Ohio (1903–1905), Senator (1915–1921)
Calvin Coolidge: City Council, mayor, state legislature, Lieutenant Governor of Massachusetts (1916-1919), Governor of Massachusetts (1919-1921) (resigned to become Vice President), Vice President of the United States (1921-1923) (became President after Harding’s death)
Herbert Hoover: Secretary of Commerce (1921-1928)
Franklin Roosevelt: State legislature (1911–1913), Assistant Secretary of the Navy (1913-1920), Governor of New York (1929-1932) (resigned to become President)
Harry Truman: County and state offices, Senator (1935-1945), Vice President (became President after Roosevelt’s death)
Dwight Eisenhower: General (had never held any political office before the Presidency)
John Kennedy: House of Representatives (1947-1953), Senator (1953-1961)
Lyndon Johnson: House of Representatives (1937-1949), Senator (1949-1961), Senate Majority Leader, Vice President (became President after Kennedy’s death)
Richard Nixon: House of Representatives (1947-1950), Senator (1950-1953), Vice President
Gerald Ford: House of Representatives (1949-1973), House Minority Leader, Vice President (became President after Nixon’s resignation)
Jimmy Carter: State legislature (1963-1967), Governor of Georgia (1971-1975)
Ronald Reagan: Governor of California (1967–1975)
George H. W. Bush: House of Representatives (1967-1971), Director of Central Intelligence, Ambassador to the United Nations, chairman of the Republican National Committee, chief liason (ambassador) to China, Vice President
Bill Clinton: Attorney General of Arkansas (1976-1978), Governor of Arkansas (1979-1981, 1983-1992)
George W. Bush: Governor of Texas (1995-2000)