College football's Bowl Championship Series (or BCS) National Championship Game was the first organized game solely between the #1 and #2 teams in the FBS. The game was first played at the end of the 1998 season and every year through the 2013 season until it was replaced by the College Football Playoff for the 2014 season. It rotated between the Fiesta, Orange, Rose, and Sugar Bowls.
Prior to the emergence of the BCS and its National Championship Game, the title of "national champion" could belong to any team that was given the label by a media outlet. Many programs claimed national championships from the same year, without any decisive game existing between the top teams being guaranteed. Bowl game matchups were contracted between conferences, and only occasionally would the #1 and #2 teams would meet by chance.
The BCS was designed to pit the two best teams in the FBS against each other in the National Championship game, and while there were many controversial decisions, the consensus is that they did so most of the time.
A total of 15 different programs participated in the 16 BCS National Championship Games. Florida State and Oklahoma are tied for the most appearances with four each, while Alabama won all three of their National Championship Game appearances, good for the most titles in the BCS era.
The BCS as a whole caught a lot of criticism for valuing traditional powers in the biggest conferences over "mid-majors"-teams from less powerful conferences. It also ran into situations where more than two teams could have arguments of deserving to be in the National Championship Game.
This first concern was addressed in 2006 by awarding the highest-ranked champion of a non-automatic-qualifying conference a spot in a BCS bowl, as long as the team in question was ranked in the top 12 of the BCS rankings or top 16 and above an automatic-qualifying conference champion. While this was considered a step in the right direction, there was never a non-automatic-qualifying conference team in the BCS National Championship Game.
The second concern led to the dissolution of the BCS as a whole-the College Football Playoff is now designed to give four teams the chance to prove themselves as the best team in college football.