The 90s.

The tail end of the NES had a lot of solid releases, including the NA release of Super Mario Bros. 3.

The SNES is still probably my favorite console of all time, with a plurality of my all-time favorite games. Certain games like A Link to the Past and Super Metroid were so far beyond their NES counterparts that it's hard to go back and play those originals. Nintendo's own output on the SNES is among their best ever, and the system in general has so many classic titles.

Nintendo's output on the N64 showed that their in-house developers were among the relative few who actually knew how to make compelling 3D gameplay experiences that weren't plagued with awful controls and/or terrible cameras. Series like Super Mario and Zelda successfully made the leap to 3D while so many other series failed in that regard.

The Game Boy also demonstrated Nintendo's ability to make handhelds that far out-compete any other offerings. The Game Boy also saw the debut of Pokemon. While I never got into the series, its early days were arguably its most popular, and it wouldn't see heights in popularity that high again until the Switch era.

The 90s was just an amazing decade to be a fan of Nintendo games.

As great as things are now, it is undeniable that the decade in which Nintendo would transition from NES to SNES…and then to N64 (and almost even GCN) is their greatest. Gaming franchises such as Zelda, Mario, Metroid, Kirby, etc etc., would go from arcade-style games over to being fully-fledged, immersive experiences which you could sink dozens of hours into. Ocarina of Time, Mario World 1+2, Super Metroid, Kirby Superstar, Smash Bros, MarioKart, Earthbound, and so many more! What a time in Nintendo’s history.

Quite surprising to see the 2010s outpacing the 2000s.
Both decades had their ups and downs, but given 2012-2016 seems largely agreed on as a dark time for Nintendo, I'd have thought the 2000s would rank higher.

2000 (and really, it was 1997) to 2006 was a dark time for Nintendo too... well, unless you're a Pokemon fan and didn't care about the home console woes and droughts, that might be seen as the golden age. For me the reason I haven't voted is because I kind of see the decades equally. I think even in Nintendo's lowest points there was always that strand of something golden, or (at least) something to look forward to.

But realistically, for me the up times were something like 1987-1992 (Golden Age: NES height, SNES release, GB early days), then 1994-1996 (uh, late antiquity revival? But basically SNES comeback and peak years), then 2007 to 2012 (Nintendo Renaissance: DS Lite and Wii), and recently 2017 to present (Modern Era: The Switch). I probably couldn't pick between any of those eras... There does seem to be a theme with XXX7 years on my model :D

If we go with decades, mine would be 2010s and 1990s by number of years, but really the most excitement for the Wii/DS was in the 2000s, but I think I was still thrilled with both systems until about 2012 even though Nintendo was pulling out hard the year before (I know, phrasing).

Me too.

But I'm about 95% sure people voting for the 2010s are voting almost exclusively for 2017-2019 (Switch hardware, Breath of the Wild, Super Mario Odyssey, Smash Ultimate, etc.) with the good stuff from before then as an added bonus. 

Switch has been a rebirth that mostly hasn't alienated the more core players (whether they're Nintendo enthusiasts or not). Even the rebirth that was DS and Wii put a ton of emphasis on more experimental, gimmicky, and casual games. 

The N64 and Gamecube did more to alienate the core Nintendo fans, Wii and DS brought many of us back.

It depends I think; the N64 lost a lot of Japanese fans as the JRPGs all jumped ship, but 1997-1999 still saw plenty of great games from Nintendo; Mario 64, Ocarina of Time, Starfox 64, Mario Kart 64, F-Zero X, Wave Race, Smash Bros, and if you count their collaborations with Rare then Diddy Kong Racing, Banjo Kazooie, Goldeneye 007, etc.

Agreed on the Gamecube era being a dark time though.

For my answer, I'll focus only on Nintendo-developed or published games, since it seems like we're not evaluating ecosystems, but more first-party output -- is that fair to say?

This is a tough one. I think @RolStoppable hit the nail on the head: "Overall, Nintendo has always made great games." Nintendo has been the most consistent developer in the history of the industry, turning out games of the year/generation with regularity for 40 years. As a result, every decade will be missing something important.

I think the 1980s are the weakest. While Nintendo developed a few arcade hits in the first half of the decade it wasn't until the NES that things really took off. And while that system was a revolution, and many of its games started franchises that endure to this day, the software pales in comparison to Nintendo products from subsequent generations.

The 2020s come next, mostly because they're a work in progress. Even though Nintendo has been firing on all cylinders for the past three and a half years, it's impossible for me to elevate a fraction of a decade over a full 10-year span. 

It's super close between the 2000s and 2010s, but I give the edge to the latter, and here's why. While 2012-2016 was a pretty rough time for Nintendo, it still gave us some spectacularly great games, like A Link Between Worlds, Mario Kart 8, Super Mario 3D World, and, in my opinion the very best game of the seventh generation, Xenoblade Chronicles. You can also throw in Super Mario Galaxy 2 and Donkey Kong Country Returns from 2010, and the amazing stretch of first-party content from the first three years of Switch, including my pick for greatest game of all time, Breath of the Wild.

The winner, to me, is the 1990s. It starts with the best NES game ever, Super Mario Bros. 3, then leads into masterpiece after masterpiece after masterpiece: Super Mario World, A Link to the Past, Super Metroid. While the N64 saw the departure of many high-profile third-party developers, it also witnessed some outstanding first-party offerings, including Super Mario 64, Ocarina of Time, Wave Race 64, F-Zero X, and Star Fox 64. But it's the Rare-developed, Nintendo-published titles that really push this decade over all others: the Donkey Kong Country trilogy, GoldenEye 007, Banjo-Kazooie, Diddy Kong Racing, Donkey Kong 64, etc.

This is actually a really good point; while 2012-2016 had its share of frustrations and a lot of droughts, the games when they did arrive were still often fantastic, plus 2010 was Wii's strongest year.

I think you've changed my mind, I'd now give the 2010s the edge over the 2000s in spite of the down years.