SNES to N64 leap was monumental. Not even like just Mario 64, like try playing Star Fox on the SNES and then go to Star Fox 64 ... like lol, it's a huge difference.

Too bad Nintendo shot the poor machine in the foot by tying it to carts-only and the dumb 64DD which never even really released properly.

I would say the switch (even though I have only played the switch twice) because it's the first time for many people (myself included) that you can actual play console games on the go. The first time I saw one on the Guangzhou subway I was blown away, truly is a great piece of hardware.

What Nintendo games have had the biggest impact on gaming as a whole (this will be very subjective)

SMB - who hasn't played this game? I wasn't around to see the impact it had back in the day, but like everyone else knows this game played a huge role in reviving the gaming industry.
SM64 - This game was the first console major 3D release, it was (as far as I know) the first Nintendo game to show off their 3rd stick which paved the way for sony and eventually Microsofts controller designs.
Zelda: OOT - this game pioneered the lock-on/targeting system for many games to come and was at the time a huge open-world console 3D game
Goldeneye - The first super popular console FPS that worked really well both in single-player and multiplayer.

Wii Sports - for many people, myself included it was the first time playing motion control video games.

SNES to N64

I don't recall better examples of games managing to be very good games in 2D and becoming one of the best games ever made when going 3D than SM64 and OOT

NES to SNES was just a refinement of capabilities, both 2D machines. - SNES Added rudimentary 3D capabilities.

SNES to the Nintendo 64 was technically and visually the largest leap. StarFox to StarFox 64 was massive... And they are comparably both 3D titles.

Nintendo 64 to Gamecube was also a refinement of capabilities with the introduction of propriety fixed function shading.

Gamecube to Wii was essentially just the same device, just overclocked with slightly more memory.

The Wii to WiiU brought forth fully programmable pixel shaders, but most of the added capability of the hardware got sunk into driving higher pixel counts anyway.

WiiU to Switch is visually a small leap, the Switch is capable of more "effects" than the WiiU and it's hardware is more efficient, but often the extra hardware gets sunk into driving higher framerates and/or resolutions. I.E. Breath of the Wild, Mario Kart, Super Mario Bros Deluxe, Mario 3D world, Tropical Freeze, Mario Party etc'.

Handhelds...

Gameboy to Gameboy colour was just colour added to the same 8bit titles.

Gameboy Colour to Gameboy Advance was like going from NES to SNES+Super FX.

Gameboy Advance to Nintendo DS wasn't as large of a leap as the SNES to the Nintendo 64 as the Gameboy Advance was faster than the SNES and the DS was weaker than the Nintendo 64.

Nintendo DS to 3DS was a refinement, but the 3DS wasn't solely relying on nearest neighbor textures either... And tended to have better shading effects.

3DS to Switch was a significant leap in every sense.

There’s a Color TV Game in that picture in the OP, one of Nintendo’s “Pong consoles”. I’d imagine going from that to NES was pretty huge. I have one (not the one in the picture), and those are pretty primitive. Other than that obviously SNES to N64, the difference really is night and day.

If we are talking overall experience then has to be the GC to Wii and Wii U / 3DS to Switch. In both instances it felt like Nintendo understood the assignment from the very beginning after previous failures. The hardware was slick, the games were great and overall they were marketing successes, the latter being an important factor in defining a console's legacy.

I think the Wii era, while flawed, redefined what the gaming genre can be. It created the sort of buzz that nothing ever did previously or probably will, in the sense that it transcended the normal "gaming" audience. This coming from the solid GC, which is an awesome console, but at the time was perceived as Nintendo losing grip of the home console market. The Wii was able to recapture that "Nintendo magic", even for a brief time, and to me it was super exciting to see as I always had a soft spot for this company. At the same time, games like Mario Galaxy and Twilight Princess were just damn good games that appealed to the normal Nintendo fan, who at the time felt that the GC swayed away from the successful formulas. After a while though Nintendo did lose sight with their gaming strategy, streamlining and simplifying every franchise they have, and after the first 2 years the Wii just could not keep up with the PS3 or 360 where developers started pouring games there. Still going from the worst sold home console to the best selling at the time says something.

The Switch jump for me might even be more impressive. I think the Wii U era was an even tougher time for Nintendo. As poor as the gamecube sold, there was no feeling that Nintendo lost sight of its ability to make great games. The Wii U era though was confusing. there were good games sure, but Mario 3D world, no Zelda and frankly the worst conceived mainline Nintendo hardware to date made the Wii U an unattractive console. The Switch on the other hand is so impressive. The hardware is so slick and is the culmination of every good idea Nintendo had, including the Wii U's tablet form, and you can see it. The games came back so hard, with open world design games. Not only did they show they can do it good, but they showed they can do it better than everyone else with BoTW. All their franchises got a breath of fresh air and it showed. This wasn't Nintendo using a "gimmick" to get some hype, this felt like the golden age of Nintendo again. For me their best ever console of all time.

If we are talking from a technical standpoint though, then I think the N64 is the only logical answer, maybe possibly 3DS to Switch (but that would discount the fact the the Switch is a home console).

1) Snes to N64 obvious number 1, as everyone here is saying, due to transition from 2d to 3d. Not only the dimensionsal jump but also how perfectly they moved Mario to 3D for the launch of the system, and did the same later with Zelda, as those two games really showed the industry what games should be like in 3D. And even though it came out after Saturn and Playstation it was so much more powerful it felt like it was an entire generational leap over them as well. Also the introduction od rumble, and the analog stick, and of course 4 player built into the sytem was huge!

2) N64 to GC. This is where we went from basic 3D graphics to really good graphics that still stand up well today when given a resolution update. This gen was the last HUGE graphical leap, as all the later ones (for the industry in general, not just Nintendo) have been a bit more incremental. N64 to GC was probably akin to the leap from PS3 to PS5. Even though Dreamcast and PS2 coming out in previous years lessened the wow factor a bit, GC games blew away DC and looked significantly better than PS2 games. I still remember playing Rogue Squadron 2 on GC's launch day and just being blown away by how incredible it looked.

3) GC to Wii. Even though the specs leap was minor as it was when Nintendo started focusing entirely on HW/play-style innovation rather than the spec arms race, the leap to motion controls was mind blowing. Wii Sports came out as a tech demo and blew the world away. How many countless months did we all play Wii Sports just cuz it was so damn fun to use motion controls. Of course motion controls ended up being something that was very innovative only for certain styles of game while most games ended up just tacking on waggle controls. But still, where motion controls worked well it totally blew away previous gameplay experiences. Also add to that Nintendo getting online play and the virtual console which were huge new features.

4) WiiU to Switch. While the technical leap was again small and similar to the GameCube to Wii leap, it was because Nintendo moved from from console to handheld hybrid (and it is especially impressive that Switch is actually more powerful than the previous gen Nintendo system considering the move from console to handheld). The fact that you can play on a TV or in handheld anywhere has really just changed gaming forever. It's hard to imagine Nintendo ever not doing a hybrid system in the future. Plus they made the controllers in a way that you have both motion controls built in (though they are rarely used) and they work well as standard controls in handheld mode or slid together in TV/tabletop mode as a normal gamepad or turned sideways to play as a tiny NES/SNES style controller so that one controller turns into two for multiplayer gaming. Really its insane how versatile they built the whole system/controller hybrid concept. The Switch really feels like what Nintendo has been working towards during its entire history in video games. Plus the move from the oppressively priced pick and choose your classic games style virtual console to the cheap full library subscription-based NSO is fantastic as Nintendo is building out their permanent classic games platform so that is just a great addition to the gaming industry.

5) Nes to Snes. Games got much prettier and much bigger in this generation leap. Remember being very excited to play super Mario World and Final Fantasy 2 when I got the Super Nintendo. They were big upgrades from the Nes games. Later on add in the FX chip and the DKC style pre-rendered graphics and SNES games were a huge leap over NES games. The acrade style 4 button pattern plus shoulder buttons really opened up gameplay as well. This was a big generational leap but it gets fifth just due to some of those 3D leaps feeling bigger and some of the later innovational leaps totally shaking up the concept of how we play games.

3DS -> Switch

Nothing else really compares. The 3DS games seem so primitive compared to Switch games in terms of both graphics and gameplay.

The top 3 in my opinion:

Color TV games to NES
3DS to Switch
N64 to Gamecube

NES to SNES is often overlooked because both are 2D. But the screen resolution quadrupled, as did the color depth. In modern terms, that's like going from 720p to 4K HDR.

Personally, the GBA SP.

It had backlighting where before that you needed an attached a light to play in the dark. It had built-in rechargeable battery, no more buying batteries! The best part to me was that it truly felt portable; where its new clam design made it fit into any pocket without looking bulky while protecting the screen, and didnt take up my entire pocket space either. I was just blown away when it first came out and the best console mid-gen redesign by a long shot. It made the original GBA looked very outdated even though it was the same system.

The only other portable devices that felt "portable" after the GBA SP was the GBA Mircro (which was an odd choice of Nintendo, but I guess they just wanted to see how much further they can push it, tho i still preferred the SP) and the PSP Go.