It's either SMB which single handedly rescued the gaming industry and launched Nintendo and the NES into the stratosphere, or SM64 which was a make-or-break launch title for the N64 and provided a blue print for a whole generation of developers struggling to make the transition from 2D to 3D.

Nah, SMB. I might be biased against the N64 (reasons), but I do consider it, as many others, the Golden Age in Gaming, but SMB did more than sell very well. It set a standard for game design, platformers, and fun > score. It moved away from arcade games, which would give birth to modern gaming consoles.

Yes without a doubt.... well SMB is close though.

OK, now that I'm full of pizza and lemonade, I can comment :)

First of all, great work with the OP. You really spent a lot of time and effort explaining and defending your thesis - something I appreciate a lot.

Second of all, if we go by your criteria, Ocarina would have to be exempt. As much as I love it, Ocarina drew inspiration from Super Mario 64. Plus, while Miyamoto was director on Super Mario 64, he was more of a producer In Ocarina, overseeing several other parties.

So then it falls to the following three games: Super Mario Bros., The Legend of Zelda, and Super Mario 64 - all of which are probably among the top ten most influential games ever made.

All are excellent choices. Super Mario 64 led the great migration from 2D sprites to 3D polygons. Super Mario Bros. made Nintendo a household name and pretty much introduced the modern video game industry.

But I think I have to give it to The Legend of Zelda. Like Donkey Kong and Super Mario Bros., The Legend of Zelda was years ahead of its time.  When it arrived in 1986 it set the standard for open world, non-linear gameplay on consoles, and would go on to influence generations of action-adventure games. Through its pioneering use of a backup battery, it allowed players to experience an enormous game world that needn't be completed in a single setting.

For me, yes.

That honor goes to SMB.

No SMB will always be, it changed the way games were designed in the industry leading to an explosion of new types of games, only Pong is more important so SMB will always be his top achievement.

Perhaps, but the first Super Mario Bros is also up there.

The only reason the N64 didn't outsell the NES and SNES was because Nintendo chose to use cartridges and forced consumers to make a choice between having variety in their library or a handful of Nintendo games per year.

N64 would've easily sold double at least if they had opted to use CDs + carts. The fact that still sold 33 million with minimal 3rd party support speaks to the strength of games like Mario 64 and Zelda: OoT and GoldenEye. 

If the Sega Master System had all the developer support exclusive like the NES had and the NES just had things like Super Mario Bros. exclusive it would have lost to the Sega Master System. 

People buy a game console to gain access to a wide ecosystem of software, not just a handful games. 

Honestly M64 is an impressive game but I find it very important to note that he came up with the idea of M64 with a demo of a Yoshi game and perfected it. Guys made later the rushed Croc games. Mario galaxy was for me a more impressive game. People were fast impressed with any platformer game in the early days of 3D platform games but mario galaxy was done in a period that it was so hard to impress people with 3D platform games.