1. Super Mario Bros 3 ; The quintessential NES game, one of the best 8bit games ever, it took everything about the Nintendo design philosophy of games and perfected it. So much fun, diversity and content on a single cartridge, married with gameplay that still feels fresh and relevant.
2. The Legend of Zelda: Majora's Mask ; One can argue that Ocarina of Time is the more important or more balanced game, but Majora's Mask is more than that. While OoT took the Zelda formula and translated it into 3D, Majora's Mask went on and from a story and gameplay point of view did fresh things and took lots of risks, making it one of the most remarkable games in the Zelda franchise.
3. Mario Kart 8 ; The best Mario Kart ever, this game is marvelous. Biggest and best track selection, best game balance, amazing graphics and soundtrack, local multiplayer dream, 200cc... Really, even without a good battle mode, this is easily one of my favorite games ever.
4. Xenoblade Chronicles X ; I don't like open world games that much, but I love Xenoblade Chronicles X. The sense of scope and the perfectly realized alien scifi world are enough to fall in love with and the first time you fly your robot up into the skies is a moment to behold. Add to that a really nice RPG system, lots of challenge in the endgame and high level of polish. Opinion: I even like the soundtrack, a lot.
5. Metroid Prime ; Exploration and atmosphere are ace, and the pacing is almost perfect. At its time, there was almost nothing like it in the console space and it holds up so well up to this day.
6. Bayonetta 2 ; This one is more SEGA/Platinum than Nintendo, but it's published by Nintendo and it's one of the tentpoles of the character action genre. While some of the boss fights might miss the grandeur of the first Bayonetta, it's more accessible and better paced overall. Style AND substance.
7. Super Mario Galaxy 2 ; This is to the Wii era what Super Mario Bros 3 was to the NES era. The Super Mario Galaxy games provide new standards for the dying genre of 3D platform games, sporting maybe the highest level of diversity and technical quality found in the genre. I only chose 2 over 1 because of Yoshi and higher challenge. I see them as one game, really.
8. Fire Emblem: Path of Radiance ; Probably a case of "my first game in the franchise therefore still my favorite". While I came to love the series in general, this still - to me - had the best mix of interesting story, level of challenge and map design.
9. The Legend of Zelda: Link's Awakening ; Zelda, in black & white, on the Gameboy. Being better than A Link to the Past and maybe the best and deepest game for gameplay and exploration on the system. The world of the windfish is a world I still love to revisit to this day, and as a kid, this was one of my absolute favorite games ever.
10. Yoshi's Wooly World ; This is more of a personal favorite because of the good times I had with this game last year together with a friend. Played through it twice. The well realized wool-style, amazing soundtrack, great level design, multiplayer and huge amount of secrets make this a game which IMO is a better game than Yoshi's Island. Also, Baby Mario annoyed the hell out of me back in the day and he's not in here
Honorable Mentions (really could be a lot of honorable mentions, so I try to make it short...):
Splatoon ; For being one of the best online multiplayer games ever and a really smart shooter at the same time.
Earthbound ; For being a game you just have to love.
Super Mario 3D World ; For the amazing multiplayer and being the Mario I envisioned as a kid when playing Super Mario Bros 3.
F-Zero GX ; For being the highlight of an amazing series.
Star Fox Zero ; For being a great Arcade shooting game with a precise and cool control layout (eff the haters!).
The Wonderful 101 ; For being so full of positive energy and clever gameplay ideas.
Wario Land 4 ; For being the most psychadelic and funny jump n'run by Nintendo and cementing Wario's character.
Donkey Kong: Tropical Freeze ; For being one of the best 2D platform games ever. And that soundtrack.
Kirby's Adventure ; Which stands next to Super Mario Bros 3 as one of the most impressive games on the NES.
Elite Beat Agents ; It was one of my favorite games for a long while, and I still remember it fondly.
This list changes all the time, as my tastes always change. But today, I would answer with these games and some of them I would've probably already put onto that list 10 or 20 years ago.