The first couple pressings of Final Fantasy 3 (6) in North America had a game breaking glitch if you used Relm's Sketch command extensively. It didn't even need to be on an invisible enemy, it would just glitch up your entire save.
Mostly, you'd just end up with an endless list of weird things in your inventory (including entries that would just say FLAG) and it could corrupt your character sprites. It would also often kill your game progress permanently because it would rewrite the game state flags internally to some non-viable state.
A friend of mine told me that he resurrected General Leo and got him in his party, but it was just him playing the game over and over, doing the glitch and hoping the memory corruption would replace the sprites of one of his characters with General Leo (and it eventually did).
The later runs of the cartridge fixed that glitch, but you could still get your game to bug out if you used Sketch on an invisible enemy. It could even corrupt your save to make unrecoverable! Awesome!
Still the best FF though.
Also, I think Stumpakopow has a list of 10-12 Nintendo games over various systems that had game breaking bugs in them that Nintendo had to issue weird fixes for. Can't find that post right now.
EDIT:
Impossible jump early in the game. And tbe turtles were the biggest thing in tbe world at tbe time too. The problem was there was no internet back then, so I was never sure why I couldn't make it, and if I was supposed to find another way across that led to days and days of wasted attempts
This jump is totally possible and not a bug in any way. [Double EDIT: Didn't know about the PC version, apparently it is impossible there] It killed me dozens of times as a kid and it wasn't until I grew up that I realized you can make that jump 100% of the time by just tapping the jump button to do a mid-jump instead of holding it to somersault. If your turtle rolls into a ball, you're using the wrong jump.