The "election" of President John Q. Adams in 1824 is one of the most interesting elections in presidential history.
Besides not receiving the majority of the popular vote (he only got 30.9%) he also he didn't get the majority of the electoral votes either. In fact Andrew Jackson technically won the election, but because he didn't win the majority of the electoral votes either, the decision on who would become the was thrown to the House of Representatives, who ultimately voted for John Q. Adams.
This election was also the last one in which the Democratic-Republicans participated in due to infighting and the eventual splitting up of the party into the Democratic Party and the National Republican Party over the results.
Despite beating Henry Clay with a clear majority of the electoral vote in the presidential election of 1844, James K. Polk actually only won 49.5% of the popular vote (Clay won 48.1%). The reason for this is because a third presidential candidate, a James G. Birney of the Liberty Party, won 2.3% of the popular vote, and might have cost Clay the presidency, because the Liberty Party was an abolitionist party, and the political party that Clay was running for president under, the Whig party, opposed the expansion of slavery (although not outlawing it).
In 1848 Zachary Taylor became the second person of the Whig party to be elected President of the United States. He also did it after only wining 47.3% of the popular vote. Probably the only reason why he didn't actually get the majority of the popular vote was because of former president Martin Van Buren, who ran for president again under the Free Soil Party ticket (an anti-slavery expansion party).
The election of 1856 was the first election in which the Republican party ran a candidate for president (that being John C. Fremont). Of course, Fremont did not win the election, James Buchanan did, but he only won 45.3% of the popular vote. The reason why neither candidate won the majority of the of popular vote is because of former president Millard Fillmore, who ran under the Know-Nothing party in that election and won 21.6% of the popular vote (although who actually would have won if the Know-Nothing party had not ran a candidate for president is unknown).
Despite being one of the most famous presidents in United States history, in the 1860 presidential election Abraham Lincoln only won 39.8% of the popular vote. In fact the only reason he won was because there were three other major presidential candidates running for president (including two Democrats).
Lincoln was also greatly hated in the south. He wasn't even on the ballot throughout most of the south, and his election was the tipping point for the start of the Civil War.
Not only did Rutherford B. Hayes win the presidential election of 1876 with only 47.9% of the popular vote, he's actually the only person to win a presidential election when someone else (Samuel J. Tilden) actually won the majority of the popular vote (that being 50.9%).
James A. Garfield barely beat Winfield S. Hancock in the presidential election of 1880, and he barely got more of the popular vote than Scott did. In fact Garfield only got 48.3% of the popular vote, while Hancock got 48.2% of the popular vote.
In fact it's even possible that Hancock may have lost due to James B. Weaver of the Greenback Party (who won 2.3% of the popular vote) winning votes that probably would have gone to Hancock.
Grover Cleveland has had a very interesting presidential election history. Not only is he the only person to hold two non-consecutive terms as president, he also didn't win the majority of the popular vote in either of the elections he won (48.9% in 1884, and 46% in 1892)
In the presidential election of 1888 Benjamin Harrison, while he might have defeated President Grover Cleveland in the electoral college (and the election itself) he didn't win the popular vote. In fact he only won 47.8% of the popular vote, while Cleveland won 48.6%.