On the European version of the Shadowrun game for the Sega Megadrive, there was a ridiculous exploit. If you follow a particular questline, you get a 50% discount on items at a certain high-end ingame shop. And if you max out your negotiation skill, which increases item sell prices and also reduces shop prices you can in effect sell items to shops for 100% of their sale price.
Somehow in that particular version the shop discounts stack, but the purchase price isn't tracked. So you can sell items for more money than you bought them for (indeed for double the money you bought them for). To the same shop you bought them from.
So that game was fun.

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Another time it was actually an intended sort of exploit, in the GBA Super Robot Wars Original Generation game. The exploit being, that the RNG seed didn't persist between saving and loading, so if you were particularly determined you could power off the handheld and reload your last save to redo a particularly bad outcome. Normally it's of limited use, since saving isn't a convenient process, and mission time limits mean it's often easier to actually figure out a good victory strategy than chase low-percentage hit chances on tough opponents.
Well one such mission is an exception. It has no time limit, and you're up against four extremely powerful boss-level enemies, with just two mechs of your own. You have a territory advantage, but by all accounts it's a fight you're meant to lose - it's the intended outcome of the story. The enemy mechs get increasingly harder to hit as their health decreases, and they get increasingly more accurate too - you're looking at single-digit chances to hit them, and single-digit chances to avoid their attack, towards the end. But they don't have HP regen, and thanks to territory advantage, you do. So, all you have to do to win, is have preternatural luck that keeps you alive for several dozen turns...
...or the perseverance and determination to keep saving, resetting, reloading, many many times, until you finally beat them. The last of the bosses congratulates you on your perseverance when you beat them, and you get some pretty powerful items as a reward for sticking it out.