Too many words have been expended on Mario 64's brilliance for any fresh contribution to made to the discourse at this point. To give it a go, though, I'd like to focus not on its creative level design and addictive gameplay, but on what Mario 64 meant for gaming a whole.
The transition from the fourth to fifth generation was big, bigger perhaps than the transition from pre-crash to post-crash consoles, and certainly bigger than anything we've experienced since (for now). Mario, the definitive 2D franchise, was at risk of being left behind, so by making the transition to 3D with such bravado, by nailing precisely what gaming would hereafter be about, Mario provided reassurance. If the reliable old plumber could do it, why couldn't everyone else?
Modern gaming begins with Mario 64. To quote Dan Houser of Rockstar games, Anyone who makes 3-D games who says they've not borrowed something from Mario or Zelda is lying."