The 8 and 16 bit eras were Nintendo's '96 Bulls run.
They started making a lot of mistakes with the 64 when they chose to stick with cartridges over CD's... which drove away all their third party support.
Mario 64, Ocarina of Time, Goldeneye, Mario Kart, Banjo Kazooie, Diddy Kong Racing, and Star Fox were still amazing games of course.
A lot of people slept on the Gamecube because the PS2 was so dominant during that time. Gamecube has gems though. (Metroid Prime, Melee, Paper Mario, Resident Evil 4, Tales of Symphonia, Double Dash, Wind Waker, Viewtiful Joe, etc)
IMO their decline began with the 64 and they officially hit Larry Holmes status with the Wii.
They're making a fierce comeback with the Switch though