Super Mario 64
Ever been enchanted by the ability to climb a tree? No? Then you didn't play Super Mario 64 back when it came out. As much as it was about fun platforming, Mario 64 was also about freedom, separating itself from its 2D brethren by sheer virtue of the number of things you could do. 2-D Mario was always about walking to the right, but in SUper Mario 64 you could walk anywhere, do anything, all at your pace. It was a completely different game with a completely different aim, and it pulled that off beautifully.
Super Mario 64 has a balance of exploration and platforming that was never again really hit in the series, which made it unique to the point of timelessness. The game is still lots of fun to play, and there's nothing that's wrong with it. A huge world filled with other, even larger worlds, great platforming segments, music that set the tone for an entire generation... on and on.
Fun fact 1: This is the first game I ever beat 100%. Odd but true!
Fun fact 2: I will still boot this game up just to go to Bob-Omb Battlefield and surf on a Koopa Shell. How about some more of that in the next 3D Mario, Nintendo?