Answer:
As of my knowledge cutoff in September 2021, there have been five instances in United States history where a candidate won the presidency without winning the popular vote. These instances are as follows:
1. John Quincy Adams (1824): He lost the popular vote to Andrew Jackson but was elected president by the House of Representatives.
2. Rutherford B. Hayes (1876): He lost the popular vote to Samuel J. Tilden but won the presidency through an electoral college decision.
3. Benjamin Harrison (1888): He lost the popular vote to Grover Cleveland but won the electoral college and became president.
4. George W. Bush (2000): He lost the popular vote to Al Gore but won the presidency after a controversial decision by the Supreme Court regarding the recount in Florida.
5. Donald Trump (2016): He lost the popular vote to Hillary Clinton but won the presidency through an electoral college victory.
Please note that the information provided is accurate as of September 2021, and there may be changes or updates since then. It's always good to refer to the latest information for the most accurate and up-to-date details.