FF6 Desperation: Tiger Break

It's not that well known, but the Limit Breaks from Final Fantasy VII were based on a hidden mechanic from the previous game. When a character's health was less than 1/8 maximum, there was a 1 in 16 chance that choosing to attack as normal would instead unleash a hidden ability unique to each.

See, for example, Sabin's Tiger Break. Letting loose a roar of pain, the royal prodigal of Figaro leaps forward to deliver a flying kick with enough force to distort the air around him.

Credit where credit is due: the background is from the game itself (Mount Kolts, where Sabin trained under Master Duncan Harcourt); character and game are (c) Squaresoft/Square-Enix.