1789—John Adams (lost to George
Washington) became 2d President 1796—Thomas Jefferson (lost to John
Adams) became 3d President 1808—James Monroe (lost to James
Madison) became 5th President 1824—Andrew Jackson (lost to John
Quincy Adams) became 7th President 1836—William Henry Harrison (lost to
Martin Van Buren) became 9th President 1844—James Buchanan (lost to James K
Polk) became 15th President 1856—Millard Fillmore (lost to Franklin
Pierce) became 13th President 1860—Andrew Johnson (lost to Abraham
Lincoln) became 17th President 1864—Ulysses S Grant (lost to Abraham
Lincoln) became 18th President 1888—Grover Cleveland (lost to Benjamin
Harrison) became 24th President (after
already serving as 22d President) 1960—Richard Nixon (lost to John F
Kennedy) became 37th President 1976—Ronald Reagan (lost to James Earle
Carter) became 40th President 1980—George H. W. Bush (lost to Ronald
Reagan) became 41st President
Reagan lost to Ford not Carter.
Before that the only real cases are William Henry Harrison in 1840 and Grover Cleveland in 1892 (and he was a former President who had a plurality of the popular vote in 1888). Andrew Jackson won in 1828 after losing in 1824 but that was in the interval between the end of the first party system (Federalist vs. Republican) and the rise of the second party system (Whig vs. Democrat), and the winner of that election had to be selected by the House of Representatives.
The elections before 1804 don't count because the second-highest vote-winner became Vice President.