I picked 2000. Most of my fond memories then.

2004.

Pikmin 2, Paper Mario TTYD and Metroid Prime 2.

Nothing better than that.

2007, if you include the bit at the end of 2006:
Wii launch
Wii Sports
Legend of Zelda: Twilight Princess
Wario Ware Smooth Moves
Pokemon Diamond and Pearl
Metroid Prime 3
Fire Emblem: Radiant Dawn
The World Ends with You
Revenant Wings
Ring of Fates
Super Paper Mario
Super Mario Galaxy
Nintendo Virtual Console
Diddy Kong Racing DS
Hotel Dusk
FF Tactics A2
Dragon Quest 4
Final Fantasy IV
Dragon Quest Monsters: Joker
Trauma Center
Phoenix Wright Ace Attorney 2
Umbrella Chronicles
Zack and Wiki
Battalion Wars 2
No More Heroes
NiGHTS: Journey of Dreams

And 2008 is a lot better than the other years listed as well:
Chrono Trigger DS
Phoenix Wright Acr Attorney: Trials and Tribulations
Smash Brothers Brawl
Endless Ocean
Super Mario Kart 6
Wii Fit
Disaster Day of Crisis
Animal Crossing City Folk
Dragon Quest 5
Valkyrie Profile
Pokemon Platinum
Professor Layton
Advance Wars: DoR
World of Goo
Fire Emblem: Shadow Dragon
Kirby Superstar Ultra
Disgaea DS
Castlevania: Order of Ecclesia
Rune Factory 2
Boom Blox (surprisingly fun)
Rock Band 2, Guitar Hero, etc... (Multiplat, but the Wii versions were the definitive versions everyone got)
Tiger Woods PGA Wii version
Mega Man 9
GRID
Civilization Revolution

90s Nintendo is best Nintendo by far.

Why is 1995 not an option?

Earthbound
Chrono Trigger
Super Mario World 2: Yoshi's Island
Killer Instinct
Donkey Kong Country 2

2010:

Xenoblade Chronicles
No More Heroes 2
Donkey King Country Returns
Mario Galaxy 2
Metroid Other M (Yes, I loved this game)
Red Steel 2
Trauma Team
Sonic Colors (a good Sonic game!)
(And though it came out Jan 2011 I'm still going to count it) The Last Story

And that's just home console.

I wanted to limit it to six years in the OP.

But that's a great choice! You could add to that list NBA Jam: TE and Ogre Battle.

Nintendo has the best years compared to Sony or Microsoft. 1998 for both Nintendo and Sony just takes the cake. Shoot on PC 1998 was amazing as well: Half-Life, Descent: Freespace, Starcraft, Starseige: Tribes, Rainbow Six. What a great year for gaming.

You missed Rune Factory Frontier on Wii, which was one of my favourites. I also liked Just Dance 1 and 2 which were both huge that year, probably the biggest games of the year. Just Dance 1 was technically released in 2009, but no one knew about it until 2010. Probably the best party game ever.

DS in 2010 had
Dragon Quest 9
Pokemon White and Black, Heart Gold, AND Soul Silver
Infinite Space
Final Fantasy 4 Warriors of Light
Ghost Trick
Miles Edgeworth: Ace Attorney Investigations
Sands of Destruction
Shin Megami Tensei: Strange Journey

On the 1990s, don't get me wrong, I really loved those years too, but they were definitely not nearly as strong as the Wii/DS years in terms of releases. Plus you had to import everything, there was a lot of bullshit.

I think Nintendo's best years were 2006 to 2010. All their good years were 86-91, 94-96, 98, and then the stretch of end of 2006-2011. Then bam, they slid hard starting in 2011, and just fell apart during the last year and a half before the Wii, and with the botched 3DS launch, followed by a botched Wii U period. I am hoping that NX is a return to form for Nintendo.

The best year ever, in my mind. You can add Burning Rangers, Shining Force III, and Panzer Dragoon Saga from Saturn too.

As a European i must say 2003 when Metroid Prime and The Legend of Zelda Wind Waker was released, two games i consider masterpieces