The Game Genie code that is forever etched in my brain is PIGOAP, it lets you swim in any level in Super Mario Brothers 1.
https://youtu.be/yjBsHyJlkRE?t=16
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There is a guy on Youtube called "Displaced Gamers" that explains how NES games work. There is an interesting episode where he breaks down how a certain item in the game Faxanadu behaves.
It's a pendant that is supposed to increase your attack power, but when you get it does the opposite. In the video he explains exactly what is going on in the code: the game was shipped with a bug.
He then goes about crafting a Game Genie code to fix the bug. It's a fascinating video:
https://www.youtube.com/watch?v=FeemO9yW-hs
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If you are curious as to how the Game Genies works, watch this:
https://www.youtube.com/watch?v=C86OsYRACTM
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If you are curious about the origins of the Game Genie, watch this: