Some of the old Rare games. While not Nintendo themselves, they are Nintendo exclusives (I think).

1. RC Pro-Am series, the series had a big influence on Mario Kart before it transformed into Diddy Kong Racing → Yes, Diddy Kong Racing was originally in development as RC Pro-Am 64. The RC Pro-Am series prior to DKC was Rare’s top selling franchise.
2. Captain Skyhawk
3. Cobra Triangle

These games are all still fun to play today.

The Excite series. ExciteTruck and ExciteBots Trick Racing were both insane arcade racers that gave you an incredible sense of speed and the jumps you could pull off were absolutely dizzying. In a weird way it kind of reminded me of ATV Off Road Fury but with a whole lot more personality and lack of concern for physics.

Sadly, the developer Monster Games merged with iRacing Games (who make the NASCAR series) so them making another game in the series isn’t in the cards. Nintendo could bring in another developer to continue the series but I’m not even sure if they did that it would have the same DNA as those two Wii titles.

This game blew my mind. I know it's a "cult Classic", but It still deserves more.

Battalion Wars 2 online multiplayer was very very good.
I feel sad for those that missed out on it.

Endless Ocean 2 is a chill Wii game to go back to and spot a giant turtle or sunfish.

Happy to see Kirby Air Riders earn more love for the series second time around.

Would love a 4-player HD version of Wave Race 64.

Would be nice to see the Kururin sequels emerge one day.

Ouendan/Elite Beat Agents are fun enough to return.

Magical Vacation on GBA getting an English translation would be amazing.

Starfy GBA games are under-rated.

Spotto!/Birds and Bombs was a fun DSi title,
as was the DSi version of Four Swords.

Punch-Out for Wii, and Wario Land: Shake It/Shake Dimension also spring to mind.
May as well throw in Virtual Boy Wario Land to complete my list.

Earthbound is one of my favorite games to, must have played it all the way through a dozen times as a kid

As far the creator is concerned the series is done so we won't be getting any new games/remakes but FOR GODS SAKE RELEASE 3 INTERNATIONALLY

I never think about Earthbound because I'm constantly talking about it. Year on year.

I think I always bring it up in combination with Metroid (NES) because both have unique Hip Tanaka soundtracks that use similar techniques for different mood-based outcomes. That is, there are a lot of silent spaces.

In fact, I'm playing it right now. Halloween, the Threed zombie war is a classic.

With that thought in mind.

Again, not Nintendo, but exclusive to Nintendo consoles: Soul Blazer, Illusion of Time, and Terranigma. These games were all very well regarded in the SNES era, but seemed to be largely forgotten by the end of the N64/PSX era, with really only Terranigma (the newest one) being talked about by that point.

I think for a while these games came up in discussion during the Wii era, because we were expecting them on the VC. They didn't arrive. Then talks went dormant again. We got an ActRaiser HD remaster, which was the first game. Shiny new assets. But, ActRaiser, while an interesting game, was my least favourite of the four... don't get me wrong, I very much like all four!

Elite Beat Agents! That one is one that was such a creative way to do story.

The WarioWare game that I really got into was Smooth Moves. That game is ridiculously fun as a party game with 8 players. Although, it's going to be difficult to see that happening again, hardly anyone drinks where I live now.

Mischief Makers. Not a nintendo game, but released exclusively for a Nintendo console, so I count it.
That game shouldve been made into a whole franchise, I need more Mischief Makers in my life.

I still see a fair bit of love for Illusion of Time/Illusion of Gaia pop up in SNES RPG circles and I hope that makes you happy.

SNES era Quintet was fantastic.