I think the real danger is franchises like Mario and Zelda becoming ultra niche and the butt of the joke just because NInty hardware are perceived as bad. In other words, many Sony, MS, PC fans make fun of Ninty games as kiddie because they can't play them and their expressed opinion affects the image of Ninty games in general. So if Mario was on xb1, steam, and ps4 the franchise could grow instead of being dismissed by non Ninty fans. 

I used to be a fan of Mario games, but lately I'm not that into them. The longer Mario remains on Ninty consoles and is perceived as kiddie, the less likely it is that I'll care for the franchise eventually when/if Ninty runs out of options.

As much as people hate to admit it, or even don't realise it, the public's opinion affects our own.

Edit: And to answer your question, definitely Mario and Zalda. Not sure about the rest.

if any company as big as Nintendo could survive the transition from first party to third party- its Nintendo. the OP mentions Atari and Sega- but do yourself a favor and name of their franchises. In terms of Atari there aren't many at all, and in terms of Sega there are only a few hugely recognized ones and even some of those are falling more into obscurity (Sonic? Phantasy Star? Golden Axe? Alex Kidd?)

Nintendo has the most powerful IP arguably in video game business with Mario. and the Pokemon (despite jointly being shared with the Pokemon Company, although I think Nintendo has a stake in the Pokemon Company anyway) are incredibly well known too

at any rate it wouldn't make sense for Nintendo to do that. They have tons of money and financially speaking are in better shape than the bigger Sony, despite Sony doing well in its video game division these days.

and it logically wouldn't make sense for them to abandon home consoles at this point. I mean just speaking towards their handhelds- they have made a lot of money with the 3DS despite is selling more than DOUBLE worse than the DS. The Wii U has been pretty mehhh in sales but even so, despite that, we're not hearing about Nintendo losing tons of money.

IN the end Nintendo is extremely careful with business. Them somehow managing to make a slight profit last year despite the Wii U performing terribly shows that they can very well hold themselves up as a first party, regardless of awesome sales

I also think some of you underestimate HOW much Nintendo makes on Consoles/accessory sales a few years into a successful generation. Like with the Wii do you have any idea how many extra Wii Motes and Mario Kart racing wheels they sold? they make loads of money at times BECAUSE they make consoles. Currently the same would apply with the 3DS, people buying chargers or even buying extra of the same system in special edition formats

Nintendo has too far valuable IP and too great of teams to even consider going third party.

It would be one thing if they were doing poorly financially or didn't have a large treasure chest of billlions saved up but they DO. There is no logical strategy for going third party at this point. Nintendo will NOT make more money from splitting software sales along more consoles than they do right now. Anyone thinking they would do not know what they're talking about. There's a reason the Wii U has stayed at roughly 300$ despite poor sales, Nintendo does whatever it takes to make profit.

But obviously they would survive. No video game company in the world (whether it be EA, Microsoft, Sony, etc.) has nearly as strong IPs as Nintendo, and there's a reason that Nintendo leads software sales each year by a dramatic amount despite only selling games on their own consoles.

I think, sure, obviously Nintendo would do well as a 3rd Party, but there is no way they would make as much from selling more software than they do from selling console variations and accessories. the accessory market adds up gigantically for systems (I'm looking at you Vita memory card, just as an example)

this.
I think some people around here have no idea how much money and profit Nintendo sometimes makes through selling accessories for home consoles or handhelds. They can make things like the stylus for the 3DS, or 'Pro controllers' for the Wii U, very cheaply and are virtually guranteed to make money whenever people buy those

Nintendo's business model is about the whole package. Their system sales, accessory sales, software sales. Obviously they are capable of going third party but how would it benefit them? they lose some control on what they're producing, they have to pay part of their sales to whomever console their games are on, and (frankly) they probably annoy part of their fanbase who loves their systems

Bear in mind that Nintendo is a pretty private and controlling company. They like to be in charge of what they're doing. 

It just doesn't make sense. Again, we're talking about a company that is technically way more financially healthy than SONY and people are bringing up the concept of them going third party? Probably the same people saying it now were saying it back during the Gamecube generation and look what happened the following gen.

Nintendo doesn't need to abandon their strategies. They just need to make more consumer driven decisions if they want to be back on top again

I dont really see how those games run the risk of becoming niche, a mainline Mario platformer has never sold less than 5 million, there is only 1 mainline console Zelda title to sell less than 4 million.

This isnt even taking 3DS into account where 2D Mario, 3D Mario, Animal Crossing, Mario Kart, Pokemon are all 10 million sellers, Smash Bros might pass that as well.

Point is that Nintendo's big franchises are far from niche even in their worst selling generation. Install base certainly grows a games potential but only if the audience is receptive towards those type of games.

Take Wii for example, huge install base but very few titles had massive growth over N64/GC installments because the increased audience wasnt all that interested in those games. Most Nintendo games dont really appeal to the shooter/sports/action audience on PS/XB so most games probably wont grow by much.

Take Mario Kart for example. Huge decline from wii to wiiu and from what I've read it's not because of quality.

You can't assume that people who buy ps/xb consoles are only into those genres. Whether people want to admit it or not, thanks to 3rd party support xb-ps consoles have a very diverse library. And you can't only look at the misleading top 10.

Make a poll and ask non ninty fans to vote. You'll see people would play ninty games if they were available on their consoles. Just because they like shooters, doesn't mean they won't also like Zelda.

Yes MK saw a decline from Wii to Wii U, thats not just becuase of install base but also because of the type of audience on Wii which is not the same audience thats on PS/XB.

Its not just the top 10, about 80% of retail sales on PS4/XB1 are shooter/sports/action. Of course there are people who like other genres on those consoles but for the most part they are pretty niche.

Polls on this site are a joke, most people just troll. Also people on this site are not indicative of the overall market. If somebody with no knowledge of gaming were to come to this site, they would assume that Call of Duty sells like shit and something like Dark Souls or Bloodborne would be a massive seller when in reality CoD sells 20 million while DS/BB sell 2 million.

Install base doesnt really make a huge difference when it comes to Zelda. Compare the NES/SNES installments to the N64/GC installments.

NES+SNES install base=110 million (61m & 49m)

Legend of Zelda-6.5m

Adventure of Link-4.4m

Link to the Past-4.6m

N64+GC install base=55 million (33m & 22m)

Ocarina of Time-7.6m

Majora's Mask-3.4m

The Wind Waker-4.6m

Half the install base but very similar sales.

If any Nintendo games did see a big increase on PS/XB than Zelda would probably be one of them but Nintendo would need more than just a few games to sell better for it to be worthwhile.

Nintendo would survive, but I would prefer for them to just close up shop instead, just to piss all the people who want Nintendo to go third party.

Wait, really? You got a source for that?

They would be fine, but I don't know if they would be able to take risks with games like Splatoon and Bayonetta 2.

This is why people should give up this notion that somehow Nintendo would be even more profitable if they went 3rd party. In the history of videogames, no previous manufacturer/publisher has given up their platform and done even better for themselves. Not one! So why all of a sudden would Nintendo be any different? People act as if Sega wasn't on the same level publishing wise as Nintendo, but they might have been ahead actually. Back when Sega were making great sports games and racing, they always turned out better than EA's offerings. Things like the Sega channel was a service way ahead of its time and worked great considering the technology available at the time.

Neo Geo- made SNK's software relevant 

Sega's consoles made their software standout 

Atari- hasn't added much since they left the hardware business.

Most of these companies only make very obscure titles or use licensed properties such as Sega with Aliens. But they are all just empty shells of what the companies use to be and the same thing would happen to Nintendo.