Money-wise: Switch era

Memorable-wise: SNES era

All three of these eras came with their own challenges and every time Nintendo succeeded despite the odds being stacked against them. Since the first and last of these three eras are spread so far apart in time, most metrics for comparison don't quite work. The major caveat is that people had nowhere near as much disposable income in the 1980s as they do today, so game sales and profits of the NES era aren't on an equal playing field with the Switch era. There's also the fact that game development was much harder, both in programming and in design, because there wasn't much video game history to look back on and take cues from. In terms of software sales, Switch still has to catch up to the Wii and DS era, so that's that.

But after typing one paragraph, it comes to my mind that there's one major problem with this whole comparison. It's that it's still up in the air whether or not the Switch era will be contained to only Switch or extend to its successor, whereas on the previous two occasions Nintendo faced much tougher conditions. And if it does extend - and the chances for that to happen are actually quite good - then the Switch era will be the easy call for Nintendo's most successful era yet.

It's Switch, easily.
Now if you want to argue you preferred software or hardware in a different era, that's more than understandable. But Switch has made Nintendo insane amounts of money.
Some may point to the NES and Early Game Boy as more successful but what big competition did Nintendo even have? Switch may be a blue ocean product but it's still competing in some ways with platforms like PS4/PS5, Xbox One/Xbox Series, mobile devices, Steam Deck, PCs, etc. There are so many viable options for gaming nowadays and yet many pick Switch as a secondary or tertiary platform or even the main or sole platform.

The Wii era of course. Because that set up for what the switch era became.

I don't see the Wii era setting up for the Switch era. If I point out something setting up for the Switch, it would be the Wii U, at least in terms of console's proposal 

Switch gets my vote also; as has been mentioned, their profits from this gen alone are greater than all previous gens combined, their games are reaching a bigger audience than ever, and with their expansion into movies and theme parks they are reaching even beyond those who game.

Nintendo are at the peak of their power; the trick now is whether they can carry on this success smoothly into the next generation.

Younger people won't understand, but it's the NES era. Nintendo completely changed popular culture in general and basically popularized a new entertainment medium that would become on par with music and movies with home video games. Before the NES, most households had a TV, a record player or stereo and even home video adoption (VCR) was still maturing at that point and that was it. Having a game console in the house wasn't a common thing. 

To do that from being a no name little Japanese brand that was basically a rag tag operation, and within a span of about 5 years (1985-1990), Nintendo had character properties that were rivaling the Walt Disney corporation, it's incredible. And they had almost like a total market share dominance in the US and Japan in particular.

A lot of people just called all video games "Nintendo" at that point, the brand was so dominant that it just became a descriptor for all video games themselves.

Imagine some tiny South Korean game maker today going from a niche little brand that doesn't even have proper global offices in all major countries to having a near monopoly on a market segment like gaming and having a character property more popular than Disney/Minions whatever and now imagine all that happening largely in a span of basically 4-5 years.

It's the double-edged sword of it could be seen as Nintendo's most successful era because they clawed their way from the bottom into video games but also the other edge is that they had little meaningful competition. That is part due to Nintendo's own ability, but largely due to the state of the market at the time. 

I did vote Switch, but NES and Wii/DS eras are valid for this thread. 

Switch financially.

NES era for changing the industry.

Switch era by far has been the most succesfull