Nintendo by a mile. The company invented or popularized a number of conventions in the console space: the cross d-pad, analog stick, rumble, motion controls, etc. Plus software like Donkey Kong, Super Mario Bros., Metroid, and The Legend of Zelda were hugely influential and, in some cases, years ahead of their time.

Nintendo, because they are an older company. lets not dismiss innovations of older gaming companies that went bankrupt. RIP SEGA (which a technically dead, but brand is bought by another company). Nintendo was not the first to innovate in motion technology though.

Has to be Nintendo, regardless of some feel about them or their recent troubles. They've also had nearly twice as long on the market to accomplish it, so it's to be expected.

Nintendo. I mean... Only by gameplay innovations they take this with ease. But even in the hardware territory, neither Sony or Microsoft have given as much as Nintendo to gaming.

The Intellivision.  It's obvious all three have struggled to come up with innovative controllers such as wiimotes, wiiu gamepad, move controllers and kinect that could rival the calculator controllers of my childhood and have failed miserably!  Long live the calculator controller!

All created in a failed attempt to copy the beloved intellivision calculator controller!   :)

Your sad devotion to that ancient controller has not helped you conjure up the stolen memory cards, or given you clairvoyance enough to find Nintendo's hidden NX...

:p. Nintendo looked deep into my soul and saw my younger self's jealousy while I  played pitfall on my intellivision and my neighbor jumped on turtles in what looked like the most amazing game machine ever!

They're very smart indeed!  Where can I preorder that mini and damn the new Zelda looks amazing.  It's like they brilliantly planned the nostalgic original NES from my duckhunt/paperboy days to bridge me to what looks like an amazing zelda for the future. Those tricky marketeers!

Microsoft, there innovation in the gaming industry is indispensable. Motion controllers and the like are just gimmicks.

Nintendo, no competition. I love Sony but most of their branding with PS has always been about one-upping, not out-innovating. The exceptions are DVD, the long con on Blu-Ray (their best move long term that I can think of), and smaller things like that.

That said, the 360 is VERY underrated in this regard. There's a lot with wouldn't have if the 360 hadn't been rushed to launch with all of these innovative concepts like overall achievements and native wireless controllers (though they still can't add a damn battery pack).