This is an epic argument though that will never end. Nintendo fans have been debating the essence of Nintendo since, well, the N64 days at least.
Funny you mentioned the N64.
Sean Malstrom once mentioned that perhaps the reason gamers are criticizing the Wii is because these are young gamers who grew up with the N64 and GC, missing the NES and SNES entirely.
If you look back at the N64 he might have a point. Many of its best titles were innovative entries in their core franchises (Mario and Zelda). Since the N64 barely had any noteworthy third party titles they kept their games coming while second parties like Rare supplied the system with new IPs that were graphically impressive.
The GC focused even more on its core fanbase and franchises, with the innovation aimed solely at them (like GBA/GC connectivity, e-Reader cards and such).
So when they see Nintendo placing its attention upon a new audience they cry foul because Nintendo catered heavily to their fanbase the last two generations and focused its innovation on them and their franchises. Hell, even a game like Wii Fit wouldn't exist during said days. It would have been deemed too risky for them.
Meanwhile, the NES and SNES catered to a wide audience. The NES in particular was sold to an audience that was burned before by gaming, and did so by creating new IPs that were easy to learn but hard to master.
Why do you think so many people remember Mario with fondness? Because it was an innovative new franchise that anyone could play.
See the relations between the NES and Wii? They both came at a crucial time in gaming and did so by providing an experience no one else dared to follow.
If you go back EVEN FURTHER you'll learn that gaming was advertised as a family/children's activity, A HIGHLY TECHNOLOGICAL TOY.
Chris Buffa of Game Daily once said that hardcore gamers were the ones that moved the industry to where it is today. He couldn't be farther from the truth.
True, hardcore games did help establish some elements. But if you look past Sony and Microsoft you'll see that there once was an Atari that gave birth and killed gaming while Nintendo picked up the pieces and ran away with it, and they did so thanks to the help of families who were impressed by the technology.