So 1876, 1888, 2000, and 2016 are won by the lost candidate.
1876 Samuel Tilden
1888 Glover Cleveland
2000 Al Gore
So a list of President could be
1876 to 1884 Sameral Tilden
1884 to 1892 Glover Cleaveland
1892 to 1900 Benjamin Harrison
1900 to 1908 William Mckinley
1908 to 1916 Theodore Roosevelt
1916 to 1924 William Taft
1924 to 2000 ???
2000 to 2008 Al Gore
2008 to 2016 John McCain