Nintendo's App Store comes in the form of the DS Shop / DSi Ware. It's not something I hear my fellow gamers talking about.
Right now, fellow gamers are certainly chatting about Nintendo, their new console - the Wii U - and it's remarkable controller. What's most remarkable about the controller is it's large 6.2 inch, 16:9, touch screen. The controller looks like a tablet with joysticks.
In fact, the controller itself can be used to play games entirely - you can do without the TV. At a glance it looks like a possible alternative to the likes of the iPad. I'm using the word 'alternative' carefully but it's certainly not a competitor. This generation of Wii U controllers don't have much in the way of internet capabilities. They use a wireless connection in conjunction with the Wii U itself.
Despite the internet limitations of the Wii U controller (and there's not an abundance of information about the Wii U's internet abilities just yet) I do think the new hardware format (which it is essentially) will breathe a breath of freshair back into the Nintendo ware concept and especially an App Store like format that so many Android and iOS users are familiar with.
I can imagine free motion comics being delivered with games. I can see Wii U controller size move trailers being made availlable; easier and quicker to download than HD TV compatible trailers. In fact, I can imagine a whole lot of possibilities.
Nintendo, however, needs to make the decision to support this ecosystem by letting people develop for the Wii U controller and 'App Store'.