Nintendo is entering mobile games, at least to a limited extent. Many people are skeptical of this. Including me. I'm skeptical of the mobile gaming market and how Nintendo's games would work in it. But thinking it over, there are a few games and pieces of software that Nintendo could make that I think would work well for the mobile market, for Nintendo, and for players.

PokeWalker

One of Pokemon HeartGold/SoulSilver's neatest new features was a little device called the PokeWalker. It was sort of a Tamagothci-style virtual pet game that complemented the main title, where your real-life walking could be used to level up Pokemon and you could get new Pokemon and items. It encouraged people to play the main game on a more regular basis, much like how StreetPass does on the 3DS. Taking this idea and transferring it to mobile devices could improve the 3DS experience without harming the sales of those games. If this came out alongside Pokemon Z for example, even as a free download, it would be a fun way of filling Pokedex entries, training party members more quickly, and reminding people that Pokemon is a big deal by topping the bestseller lists.

WarioWare

Mobile Games encourage shorter play sessions than even handheld games. Many games that succeed on mobile devices would be considered minigames on other platforms. So in a way, WarioWare's 5 second microgames would be at home on mobile devices. The touch screen and gyroscope would provide more than enough possibilities for interaction, especially after how well simple tilts and touches have worked since the GBA days of WarioWare. If Nintendo for some reason went mobile-only, this series would likely have the best transition.

Mario Kart TV (And Other Video Sharing Apps)

Remember this part of Mario Kart 8? Where people could share videos of their races and connect with Miiverse? I didn't, because when I watch Mario  Kart footage, I don't want a 60 second limit. Seriously, most races take me at least 2 minutes. But that aside, apps that could share up to a few minutes of gameplay would be cool ways to spend time on mobile devices. And it doesn't have to just be Mario Kart; imagine if Super Smash Bros 4 updates stopped making the replay feature useless. Along with Splatoon, you would have three games that can be patched and would provide great short videos for viewing anywhere. Maybe Pokken Tournament would also be a good candidate.

Hyrule Historia (And Other Lores)

Hyrule Historia was a surprise hit a couple of years back, but it turns out that people really wanted official word on the lore of the Zelda universe and the real-life development of the series. And although it might be a bit much to hope for Nintendo to become a major author, I think similar projects for various Nintendo series, especially those with long histories and deep universes. Obvious candidates include Metroid, Pokemon, and Fire Emblem, which have both extensive histories in real life and plenty of in-universe tales to tell.

Are any of these good ideas? What Nintendo-made products would you like to see on mobile devices?

Wouldn't Pokemon Go make a PokeWalker app redundant?

I want a Nintendo-themed Hearthstone game. That's everything I want.

But I guess Wario Ware would be cool too.

I could see Rhythm Heaven being a pretty good fit on mobile too.

Did you play the DS version of Rhythm Heaven ? It was awful, because the touch controls aren't enough responsive for the demanding gameplay of Rhythm Heaven. You absolutely need buttons to play it.

Yes for Hyrule Historia!

Whaaaat? Touch controls are as responsive as buttons in the Rhythm Paradise series. If there is a difference, is minimal. And I've perfected all the entries in the series except for the 3DS version which I cannot wait to be announced for the west.

As for the main topic, I could actually see Mario Kart on smartphones. Motion controls worked pretty well on Wii, 7 and 8 so they could do it. But of course, Nintendo is not going to put such a series on mobile. It would seriously damage sales on consoles.

Warioware and rhythm heaven are the most obvious games for mobile as they fit perfectly. I loved r.heaven on the ds and I think people would like it, you can play 5 min or 2 hours, it's addictive and fun.
Also, one of the biggest dissapointment I had with the wii u, kirby, would be perfect for mobile as well. I loved how the game looked but I couldn't stand the gimmicky gameplay so I had to pass. But that game fits on the mobile market more, maybe not as a full game but imagine the same mechanics only with changes like shorter levels or focused on defeating enemies and bosses or collecting some specific items.
Nintendoland also had perfect ideas that could work as small mini games for mobile.

I think what Nintendo should do is focus on the way people play on mobile, how playing on mobile is as opposed as a console (tap the screen, move the phone in a racing game etc) and then create some unique games on their own, with their ip's.

They could do so many great things. Also, miitomo I think could be great. I love mii's and if they do it right they could make billions.

Along with your suggestions, there is definitely a lot of games that would be perfect for mobile... Planet Puzzle League, Pushmo, Nintendogs+cats, etc..

but it looks like Nintendo wants to make new mobile games/apps rather than making direct sequels of some of the mentioned titles