The Marcus/Eiko stat bug is a bug which occurs when leveling Marcus in Final Fantasy IX causing some of Marcus's stat growth to be added to Eiko's without affecting her level, enabling her to obtain much higher stats.
The bug is a result of Cinna, Blank and Marcus being early temporary characters whose templates are later used for Quina, Amarant and Eiko, respectively. In each case, if the temporary character levels, their stat growth is transferred to their counterpart. For the case of Quina and Amarant, they will become whatever level Cinna and Blank left the party at if it is higher than the party average. Since Quina's and Amarant's stats grow when leveling themselves, it is not beneficial to level either Cinna or Blank.
The bug is most beneficial if one plays a level 1 game and levels Marcus to level 99 during his time with the party. Doing this, Eiko can potentially gain over forty stat points (combination of Speed, Strength, Magic and Spirit). She is the only character able to max either Strength or Magic, and as a result can have the highest HP and MP in the game. She will also have the most Magic Stones.
Marcus is in the party during the only part of the game where an endless stream of enemies will approach the party. This is immediately following being able to obtain the Blood Sword, which allows Marcus to regain health when he attacks. Using a turbo controller, one can leave the game on for several days to allow Marcus to level himself to 99 with no in-game risk.