2003 was actually one of Nintendo's worst years ever. It was the first time they ever reported a quarterly loss.

https://www.ign.com/articles/2003/11/14/nintendo-reports-loss

Anyway, best years:
1983 - The introduction of the Super Famicom kicked Nintendo into the mainstream in Japan.
1988 - The NES goes mainstream worldwide with Super Mario Bros, Tetris, and World Cup bundled with NES, and a similar bundle with Super Mario Bros, Tetris, and Duck Hunt in the US.
1991 - marked the release of the SNES in NA, and Super Mario Bros 3 in Europe.
1994 - the year Nintendo won the 16-bit era, and that was thanks due to a revolution in quality thanks to games like DKC and Final Fantasy 6.
2006 - DS Lite and Wii finally rescued Nintendo out of the pits of an almost 10 year decline. Killer app releases of New Super Mario Bros and Wii Sports, and the worldwide introduction of Touch Generations.
2008 - Nintendo's highest selling hardware year to date. Nintendo shipped 57 million units of hardware, and over 400 million physical retail software sales.
2017 - And while there was a second valley between about 2012 and 2016, 2017 continued where Wii/DS left off in 2011. Two major killer apps in Breath of the Wild and Mario Kart 8.
2021 - Animal Crossing proved to be a massive killer app this year, breathing new life into the Switch that sustained it for years to come.

Yah but 2003 had F-Zero GX tho

The thing is that game only shipped 692,000. A decline to about 1/4 the sales of the original F-Zero on SNES. So, while it's good for the few hundred thousand players that actually bought it, the game did little to help Nintendo. Although, the problem might not have been the game, but rather the Gamecube.

Perhaps that one will see the light on Switch 2.

Oh I know it was a commercial failure. It was freaking awesome though. A real shame.

HAHA! Well, there you go! That didn’t take long to announce! 😄

I'm also gonna defend 2011 a little.

It wasn't one of their stronger years, but between Xenoblade Chronicles here in PAL land, Skyward Sword, Rayman Origins, Modern Warfare 3, Kirby's Return to Dreamland, FAST Racing League, and de Blob 2, my Wii still had some life left in it; it was definitely way better than the likes of 2016.

I'm going for personal vibes and feel, how I felt during those years. LAck of games palyed a role but also Nintendo's positioning in the industry

Best

2017 - Probably my best ever Nintendo tear. Two generational games, particularly BoTW, that clawed Nintendo back to relevancy after the dismal Wii U years, and the sort of Wii Branded, family friendly non-hardcore image it created for itself. They proved that they could not only make great games, but literally shake up the open world formula on their first try! By the end of 2017 the switch outsold the Wii U. Quite a statement, quite a year, hardcore Nintendo fans were back!

2007 - If there is a console from the 7th gen consoles you would want to play, it would be the Wii. It's so unique and there's nothing like it so much so that Sony and Microsoft wanted a piece of that pie. Mario Galaxy was elite and they battered Sony in releases (something that would change) and proved they got it right. 

2001 - I LOVE the Gamecube, and Smash + Luigi's Mansion was a lovely combo to start off the console. It's a shame they couldn't maintain momentum in 2002 as Sony just blew away the competition. Delays hurt the Gamecube but that initial release window was an awesome time and felt magical.

2008 - Wii and DS at their peak. Anything more to say? The triple wammy of Smash, Mario Kart and Wii Fit was insane to start the year. One of my fav times being on this forum. Also the DS kept releasing gold. The Layton games are still one of my all time favs and this year brought the first one. Lovely year to be a fan

Worst

2015 - Probably the worst year I've ever experienced as a fan, and almost gave up on the company. Barely any games of note that had an impact on the industry, and obviously Iwata's passing was crushing. It did feel like Nintendo was irrelevant and it's crazy to see them go from this to the peak that is the Switch which was arguably one of the best eras Nintendo every had. 

2016 - The best thing about that year was the showcase of BoTW and the Switch which at least gave Nintendo fans some hope which was missing the previous year. Also remember Star fox? Yikes

2012 - I remember getting NSMB 2 and thinking, wtf are Nintendo playing at. The Wii U E3 event looked lame, and the launch was really uneventful, like Zombie U was hyped up. 

2013 - I remember looking forward to E3 and seeing Super Mario 3D World. It's the game I look forward the most along with Zelda every console generation, and it sucked. Like 2011, I felt MArio always innovated but they took a step back with this one. In retrospect it's a fun game but really linearised the formula which made me feel that Nintendo was stuck in the Wii mindset of making games too easy and dumbed down. 

2011 - Just a sluggish year all around and a disappointing 3DS launch. 3DS kinda got it back together but it feels like the damage was done and the hype was gone. I think it also was stuck in an era were mobile games began to dominate. The Wii that year was abysmal and Skyward felt like it dragged Zelda from a game that defined a generation to a gimmick beta test. As much as I love the Wii this just was not it. At least we got Super Mario 3D Land