One time, in 1800, the U.S. Presidential Election resulted in a tie. At the time, Thomas Jefferson was running against incumbent President John Adams.
The election exposed a flaw in the Constitution, because the Electoral College was authorized to vote for two names for President. Therefore, Jefferson and his running mate, Aaron Burr, both received 73 Electoral College votes, because there was no role to indicate which one is President and Vice President.
This issue was brought to the House of Representatives, resulting in 36 different rounds of votes – coming out with Jefferson as the winner.
After this mix-up, the 12th Amendment was ratified explaining that electors make a discrete choice between their selections for president and vice-president.