In an interview a while back Iwata said, 

http://www.gamespot.com/articles/nintendo-s-next-console-and-mobile-will-be-like-brothers/1100-6417496/

Finally, Iwata said he remains unsure if the form factor of its next platforms will be integrated to establish some kind of hybrid system. Instead, he said the opposite might be true; that the number of form factors could increase in the way that multiple devices can run iOS and Android. This will all depend on consumer demand, he said.

"The point is, Nintendo platforms should be like those two examples," Iwata said, referencing iOS and Android. "Whether we will ultimately need just one device will be determined by what consumers demand in the future, and that is not something we know at the moment. However, we are hoping to change and correct the situation in which we develop games for different platforms individually and sometimes disappoint consumers with game shortages as we attempt to move from one platform to another, and we believe that we will be able to deliver tangible results in the future."

I think there will be demand for both a handheld and home platform, and if Nintendo uses a modified Android OS maybe even mobile will be integrated, as a potential open-platform in which they release some of their smaller games on. 

So at least two in my opinion. Some people have argued that it would be a single platform that can be attached to the television and used as a handheld device. I don't think Iwata and Nintendo are leaning toward that though. 

I say two, one handheld and one console and the console will have significantly more power than the handheld and it will have its own sets of games that wont be on the handheld

Two. The Fusion system will work on both handheld and home console. Also, this machines will also play the mobile games (but not the other way around).

I agree from my view the fusion aspect is the unified OS.Seperate HH and Console

I could see Nintendo trying to implement a similar strategy as Apple has with iPod/iPhone/iPad/Apple TV. So maybe 3 different handheld skus and a TV version with slightly different power levels but all able to play the same games just at different graphic settings. For example

NX Mini-4 inch, 480p screen, $149.99
NX Portable-5 inch, 720p screen, $199.99
NX Plus-6 inch 1080p screen, $249.99
NX TV-1080p, $199.99

Then after 3 years do upgrades to them, Mini-720p, Portable-1080p, Plus/TV-4k. Another upgrade 3 years later to Mini-1080p, Portable-4k, Plus/TV-8k.

By the time that final upgrade has its 3 years, we're looking at a decade from now so who knows what gaming will be like then.

At least three. They're making a system for China.