Quote Originally Posted by Squall of SeeD
Final Fantasy VI was actually the first to introduce this concept. The first form of this concept were VI's Desperation Moves that characters would occasionally perform when they had been wounded and sent into critical HP levels.
In FFVI, the desperation attacks occurred too randomly to be used to any strategic effect; they were just something to save your skin if you were about to die and got lucky. FFVII was the first game in which this kind of attack could actually be used strategically, and it's that aspect that the following games have continued.