The 1824 Presidential Election was the first where various States, not all of them that would be the next election, counted the popular vote in determining the distribution of electoral votes. JQA was facing three other opponents in the general and all from the same party since the Federalists were no longer a threat as a national party to the Democratic-Republicans. Andrew Jackson received a plurality of votes in both popular and electoral votes, with JQA in second place. Third place in the Electoral College went to William Crawford, the Secretary of the Treasury, and 4th place went to Henry Clay, the Speaker of the House of Representatives. In the popular vote column the two switch finishing positions, but once again it is the electoral votes that matter. Since there was no clear majority of electoral votes, the Constitution instructs that the House take the top 3 vote getters and vote on them with each State having one vote, so delegations with more than one representative would have to vote among themselves to determine whom they cast their vote for. Crawford suffers a stroke, which makes the House competition between JQA and Jackson, with Clay as presiding officer of the House. Supporters of Jackson believe a "corrupt bargain" was struck between Speaker Clay and Secretary of State Adams, the presidency for appointment to head the State Department, then a stepping stone to the presidency (James Madison and James Monroe, both incumbent secretaries of state before being elected president). Since John C. Calhoun was the vice presidential nominee for both Adams 6 and Jackson, he won a majority of electoral votes in the General Election and later in the Electoral College vote, so there was no need for the Senate to determine the vice president, but they would have had either Adams 6 or Jackson had their own vice presidential candidate. JQA won the House vote and Clay eventually became the secretary of state and Jackson literally began campaigning for 1828. His supporters took up the label Democrats and the Democratic Party was born. Adams 6 and Jackson would face each other again and Jackson would finally get the presidency with 56% of the popular vote and a clear majority in the Electoral College.
52 years later in 1876, the nation would experience another unusual election. Samuel Tilden, the Democratic nominee once again won the popular vote while Rutherford B. Hayes, a Republican, won the Electoral College votes. But it was determining the distribution of electoral votes that was the problem in 1876. Various State governments in the Reconstruction of the South after the Civil War sent two sets of votes representing their State, so a commission of Democrats, Republicans and independents met to determine which candidate got which electoral votes. A deal, or rather, a compromise was made just days before the March 5, 1877 Presidential Inauguration. The Compromise of 1877 allowed Hayes to receive the electoral votes, if Federal troops are removed from the South, thus ending Reconstruction. Since March 4th landed on a Sunday, the public ceremony would be on the 5th, fearful of retaliation by Tilden supporters so closely after the Civil War Hayes was sworn in on the 3rd in the Red Room of the Executive Mansion with President Ulysses S. Grant by his side. They of course had nothing to fear as the inauguration came and went without a problem. Hayes promised to serve just one term and Tilden never faced the voters again, dying ten years after the election.
Two years after Tilden's death in 1888, the nation once again had another unusual election, but that's about it. The 1888 Presidential Election is pretty straight when compared to 1824, 1876, and 2000. President Grover Cleveland won the popular votes while his opponent from Indiana, Benjamin Harrison, grandson of William Henry Harrison, won the majority of votes in the Electoral College. The Democrat won the popular vote, but the Republican, once again, won the Electoral College. No questions asked. But like in 1828, 1892 would pit the 1888 candidates against each other again, a rematch. And just like in 1828, the candidate that won more votes in the previous election came back and won. Former President Cleveland became the first, and so far only, former president to win a General Election and thus serve two non-consecutive terms. Harrison 23, like Adams 6 and Tilden, never ran for the presidency again after their defeats the second time.
It wouldn't be until the year 2000 that nation would experience an election that doesn't go just right. Vice President Al Gore was hoping to do what Vice President George Bush did after 8 years as VPOTUS, and he came pretty close. Gore won more than 500,000 popular votes but it came down to 537 votes in the State of Florida. The election was so close that Gore asked for a recount, but George W. Bush, the presumed winner of the Florida electoral votes, stakes a claim that he won the State. The Florida Supreme Court sides with Gore and the recounts in various counties goes forth, until the Federal Supreme Court sides with Bush in the ruling of Bush v. Gore. Yes, the States' Rights party, went to the central government to decide a local matter. With the Supreme Court's ruling, Gore could do nothing but concede, again. Had the September 11, 2001 terrorist attacks not happened, former vice president Gore might have followed in Jackson and Cleveland's footsteps in winning a 4-years-later rematch. But instead Gore went the way of Tilden and did not seek the office where more voters liked him over the Electoral College winner.
With George W. Bush's reelection to the presidency in 2004, another close and controversial election, Bush 43 breaks away from these other popular-vote-loser-presidents. Unlike Adams 6 (another member of the POTUS Father/Son pair) and Harrison 23 (another member of a POTUS dynasty, but grandfather/grandson), Bush 43 would not be defeated in an election. Another difference of course is those two faced a rematch. Bush 43 didn't run against Gore in '04, but Massachusetts Senator John F. Kerry. While the votes in Ohio are questionable, and determined the presidency in 2004, just like Florida was in 2000, but this time Bush 43 won both the popular and electoral votes. His victory in '04, finally getting the presidency with the popular vote, broke the whole popular-vote-loser-president never winning the popular vote. This is very similar to what vice-presidents-turned-presidents through death and assassination and their turn at the top of the ticket and winning an election in their own right. Whereas John Tyler, Millard Fillmore, Andrew Johnson, and Chester A. Arthur never won the presidency at the top of a presidential ticket, Bush 43's break from tradition like Theodore Roosevelt, the first vice-president-turned-president that went on to be renominated and win the presidency in his own right. Calvin Coolidge, Harry S. Truman, and Lyndon Johnson would follow in those footsteps. Gerald Ford would come close, but lose to Jimmy Carter.