Well; knowing Miyamoto, if it's an existing genre it'll no doubt be something different to how it's usually been applied before (compare Pikmin to other RTS, Wii Sports to other sports games).

He has said he'd like to do an FPS, but I doubt it'd be a Halo style game. I dare say it would be something more along the lines of Portal (ie. puzzler with shooter mechanics), and would probably heavily feature asymmetric gameplay for the multiplayer. Possibly some sort of on-the-fly dungeon design; so gamepad is playing Dungeon Keeper and TV is playing Doom trying to get into the dungeon. Given the prevalence of futuristic and modern themes in shooters, I think we'll see a different setting. Maybe a 3PS given he's said he liked the controls of Metroid in Nintendo Land, so we may be something like that in terms of control scheme.

So my guess:

First/Third Person Shooter
Puzzle more than combat oriented play
Asymmetrical multiplayer, 4 v 1 competitive
Not a standard modern/futuristic setting

And for the record I would play the hell out of Dungeon Keeper/Doom mash up style game (although I don't think that's what we're getting)

Not Mario for fraks sake not anything mario related.

I think it's a good time for that Nintendo shooter. Wii U can't sell much worse than now, so not much will be lost when the game fails to move a decent amount of hardware, and hopefully Nintendo will learn the lesson.

I predict it will be something with a lot of colors.

It'll be little more than a puzzle game, or a simple platformer or something like that, probably digital-only even. Miyamoto already said that the only things he'd still be developing are smaller projects with smaller teams.

Which he will base on his childhood experience of when he was out swimming with his uncle.

A puzzle game.

An FPS, because they need to explore more genres for the sake of variety, and to be honest it would be really interesting to see an FPS by Ninty.

I'm expecting to see the shift towards the smaller games now, so maybe an e-shop title? Tower defence or something.

I want that damn cookie so I will predict.

I say that the new IP Miyamoto has in store is... non-existant! Yeahd guys it doesn't exist! He was just messing around with us! He will announce his official retirement on april 27th.