Nintendo's most influential games are probably the ones that created entire genres, like those that have already been mentioned (SMB, Zelda, etc.). But my favorite Nintendo games are the ones that reinvented existing genres.
1) Super Mario 64 -- Brought platforming into 3D and showed what a platform action game could be in real 3D. Ocarina of Time could easily take this slot too.
2) Super Smash Bros. -- Completely turned the fighting game genre on its head, with battle items, interesting arenas, 4 player simultaneous battle, mixing characters from completely different backgrounds, and a single player experience that was so much more than just one-on-one fights until the boss.
3) Metroid Prime -- Super Metroid built on the foundation of the original Metroid and Zelda II, but Prime merged this gameplay style with the most popular, First Person Shooters, to create the first First Person Adventure. It put the player inside Samus's power suit and really gave the Metroid series the sense of immersion, and therefore the emotion that it needed.
