Hard one. I think the DS, Switch, Wii, and Gameboy shook up the norms of the industry more than anything else, but the N64, SNES, and NES all have very powerful arguments.
The N64 really showed the industry how to do 3D gaming. Unlike the Wii it had the glaring weakness of cartridges - which caused a tremendous spike in cost and created a clear development hurtle that didn’t exist on other consoles. 32MB or 650MB, when redbook audio, rendered graphics, and FMV were able to create better looking and sounding games than all that extra power the N64 had, it became clear that Nintendo’s first dynastic rule was over.
The Wii’s weakness of lower horsepower also proved to be a major strength, again, pricing for the Wii, on top of its new interface helping to shape one of video gaming a biggest killer apps in history, made it - for a time - the most compelling home console ever released.
While the Switch will top the Wii’s sales, the Switch is something new and different, first of its kind. It’s a hybrid, basically sells like a handheld and generates revenue like a home console. It might prove to be the most compelling form factor of a dedicated video game console in history. People can own it as a singular console, carry it around, then plug it into a TV and play with friends like a home console. This is why Mario Kart 8 on Switch, a mediocre Mario Kart game on Wii U, is the best game of the franchise on Switch.
GameCube was basically PS2 junior, a clonebox with missing features, a less functional hand-hurty controller, and (once again) an inferior media. it is the most irregular of Nintendo consoles in that it’s the only one which basically tried to be like the competition rather than being what it needed to be. I see it as the least-Nintendoish of any Nintendo console. I also find it’s fans to be only distinguishable from Sony fans in that they like the letter N better than S - they often whine about Nintendo screwing up when they do anything different from Sony. It’s like they want a PlayStation, but only their fanboyism holds them back; they’re not actually interested in the Nintendo lineage of consoles, OUR dynasty, which currently rules thanks in part to great Kings, like the DS, Wii, and currently the Switch.
(Sorry, been watching lots of medieval shows lately)