Final Fantasy XIII makes use of enrage timers from at least Chapter 10 onwards. The game never explicitly says so, but if you reach 20 minutes in a boss battle the boss will cast a 3-minute (I believe), unremovable Doom on your character. If the boss isn't dead before the timer finishes, you die. Even happens against the post-game "ultimate" boss too. That'll teach me to play it safe and turtle. :rolleyes:
Can't really think of anything older than that besides specific one-off encounters such as Sin's Giga Graviton, though.
