Sony is making PlayStation one of its focuses so I highly doubt they're going anytime soon. Especially since they just plunked down 300million for Gaikai.

Microsoft is the same as Sony, Xbox is becoming one of the focuses of the company and they're using it to sell other products and services.

Nintendo is a gaming company with mountains of cash from this gen, I don't thing they're leaving even if the WiiU is a total flop.

So where's the "none" option?

Sega.

If anything, maybe either Sony or Nintendo will start to only do software. Microsoft won't die. Nobody will exit the market completely though.

I think Nintendo will be the only one that carrys on in the traditional way whole heartedly,

I think MS next console has a good chance of just being a Windows RT machine of some kind, so there gaming can me done across all of there devices. And they will have finally got a Windows box in the living room, which has always been one of there goals.

Sony is already making roads into making there older catalogue available on other devices like Android and i expect Windows and IOS will follow, and with the acquisition of GaiKai, i beleive there will be an option to just have a streaming version of PS4 on any wireless device that can connect to a bluetooth controller.

Simply impossible to predict. There's so much happening in the gaming business with integration of platforms, revenue models, cloud gaming and new competitors coming in (Apple, Google).

Hard to say, and the most sensible answer would be none of them. It's a very lucrative business.

But, since there is no fun in that, I'll guess and say that it will be Nintendo who leaves the home console hardware market.

Both Microsoft and Sony see their consoles not only as consoles, but also as multimedia devices that can also be used to sell some of their other products, gadgets like Kinnect and software like Win8 in the case of Microsoft and TVs, HiFi, etc as well as their music and movie services in the case of Sony.

That leaves us with Nintendo, which sees the consoles as a way to sell their games. What effect does the hardware side of their business have? As of late, it only makes them lose money. Sure, having their own console was a good move in the past but now it's going against them. Because of this, and the pressure of their shareholders to develop for other devices (mostly smartphones), they are the most prone to quit the hardware side of the business and go third party.

But as I said, I don't expect anyone to leave anytime soon.

Sony is in the worst position.

Assuming the 'console', tradionaly stays primarily a gaming machine. Sony absolutely need a possible successor to the PS3 to be (financially) very successful, otherwise they're in big trouble. Sony has a bit of a dilemma. They don't have the money to go the 'powerhouse' route again, but they also can't afford to lose market share to Microsoft if they don't and MS does.

Both Microsoft and Nintendo have too much cash to go under even if they screw up big time. Microsoft's software divisions are easily capable of keeping the XBox afloat if it isn't profitable and Nintendo's handhelds will keep them growing and strong if the consoles are weak, like the GameBoy did during N64 and GameCube era's.

Also, it's about we saw some action again. Statistically it has been too long already for any drop-outs. ;)

I can see a few different situations. The only constant between them is Nintendo - Nintendo really isn't going anywhere. They've proven that repeatedly. Their IP is too powerful and their studios are just too good. Even with zero third-party support, Nintendo would be able to sell a good 10 million units of hardware (assuming they don't go bat-shit insane with it) and make a profit on each unit, plus a profit on each of their big games. Of course, there are theoretical ways for Nintendo to not survive the next generation, but I consider them unlikely enough to dismiss.

So, what are the situations?

1. Sony is forced by financial pressures to drop quite a few things. Their gaming division gets sold off to some other company, who will focus on software only. There's then two possible results from this point:
1a. Microsoft leaves the dedicated gaming hardware business - after all, they entered to protect themselves from losing the gaming business from PC to the Playstation. This likely leads to a computer hardware company stepping up to make a dedicated "gaming PC console" that is designed to run Windows games in a dedicated fashion.
1b. Microsoft sticks in the dedicated gaming hardware business, but establishes an online delivery system to effectively merge their Xbox and PC game development into a single Xbox infrastructure.

2. Microsoft focuses too much on raw power in their next console, tries to charge an outrageous price (more than $600), and it flops badly. MS quickly withdraw to their PC business, and Sony brings in enough support from those who want more power than the Wii U to survive and be slightly profitable (I see Sony not making the same mistake they made with the PS3 - expect a much more modest power level with a more reasonable price, of the order of $350-$450, with only a slight loss on early consoles). Note that, in this case, MS likely sells off their game studios, and refocuses back on OSes and more business-oriented stuff.

3. A new challenger (not the Ouya) comes up, and starts to sap MS and Sony sales. It could, for instance, be Valve. The new challenger provides a more developer- and publisher-friendly environment, and MS and Sony lose exclusives. Nintendo is forced to adapt (and, in my opinion, holds on to what support it has from certain third parties, including Ubisoft, Capcom, and Square Enix). It's possible, in this scenario, that MS and Sony even go so far as to join forces - picture Xbox Live + Playstation - but it's not likely (think 1% chance).

4. The least likely of the situations I consider worth mentioning - Ouya manages to perform well, and forces a significant change to the industry. This change harms Sony's business, but overwhelms MS's business, as a standardised gaming PC saps MS's bread-and-butter genre, the FPS. Sony ends up focusing primarily on Japanese gaming, and allies with Square Enix quite strongly - it becomes the RPG console of choice. Nintendo isn't particularly affected, however, as third parties would see Nintendo as the "safest" bet, with the Ouya and the Sony system becoming the places for the risky stuff. Note that I'm not saying it would help Nintendo, just that Nintendo would be stable, unlike situation 3, where Nintendo has to adapt.

EDIT: I just realised I didn't emphasise - this is the set of situations in which at least one of the three doesn't survive. I actually think all three surviving is the most likely outcome, although I'm undecided on whether Sony and MS continue into the following generation.

MIcrosoft

People will wake up and don't wait for Halo 2387623 and CoD DLC
BÄM no interest any more and Sony is going back up to the old primetime where people were interested in million different genres.

This would happen if the world would be full of good people.

I think all will survive next generation, but, if i had to pick one to exit the market in 5-6 years i would choose MS.
Xbox is irrelevant in Japan and i just don`t see that changing ever.
In Europe, the only real strong market seems to be the UK, if i recall correctly and in remaining countries Wii and PS3 have a good presence.
The States is the real market for Xbox 360.

The reason i pick MS is because the company has become too dependant on those two markets, specially the US.
37 from the more than 67 million Xbox 360`s sold to date are from North America.
My belief is that Nintendo will do a better job with Wii U and Sony won`t make the same mistaked with PS4.
Another problem might be that by the end of Xbox 360`s life, the console will have 3 ways to interact with the console: normal controller, kinect and smart glass. Will MS keep them on Xbox 720? Most likely. But then again what can MS introduce to Xbox 720 that is "fresh" not just for consumers but that really distinguishes it from Xbox 360?