Any casual soccer fan has at least heard of the term "golden goal", the rule that states that when a game ends in a draw and goes to overtime whoever scores first automatically wins the match. The rule was not mandatory, but could be adopted by the organizers of any tournament.
The golden goal rule can be traced back all the way to the 1800's, but it was only officially adopted by FIFA in 1993. The first time it was ever used was in the 1993 FIFA U20 World Cup, when Australia eliminated Uruguay in the quarter-finals. When the MLS was founded in 1996 it immediately adopted the golden goal rule for its playoffs. It was then first used in major international tournaments in the 1996 Euro Cup and then in the 1998 World Cup.
What is very often forgotten, however, is that between 2002 and 2004 FIFA introduced the "silver goal". A rule where if a team scored during extra-time, the game would only end at the end of that half, or if that team widened their lead to 2 goals.
The silver goal rule was first notably used in the 2002/03 UEFA Cup Final (modern day Europa League) between Porto and Celtic. After a 2-2 draw Derlei scored for Porto in the 115th minute and instead of the game instantly ending it was played until the 120th minute. In the following season Ajax eliminated Grazer in the UEFA Champions League qualifying rounds with a silver goal as well.
It was perhaps most famously used in the 2004 Euro Cup semi-final between Greece and Czech Republic, when Greece scored in the last seconds of the first half of extra-time and the second half didn't need to be played.
At the end of 2004, FIFA declared both the golden goal and the silver goal failed experiments and announced their end. Their purpose was to give teams incentive to attack and score but instead it just caused teams to be more cautious and play conservatively. Because it had already been agreed upon previously the golden rule was actually used one last time in the 2006 FIFA World Cup and that was it.
Interestingly enough the NCAA, which has no affiliation to FIFA, still applies the golden goal rule during its play-off matches to this day.