It would either have to be Nintendo or Microsoft in the last decade. No matter how much I dislike some of MS' decisions, they've come to define much of what we know as the "modern" gaming market.

And Nintendo, well, that's quite obvious. They brought more physical innovations than MS.

Microsoft did a really good job with the original xbox. As many have mentioned, they got the whole online play going and achievements later on were a great add-on to give more value to games and even for bragging rights.

The gameboy also did a lot of portable gaming, I remember using my Gameboy SP for hours, everyday.

Sony's PS+ has also been game changing in my opinion. It bring so much value, not just to one console, but all current sony consoles across the board.

I'd be hard pressed to choose against Microsoft because of the accomplishments of their online service with the Xbox 360. They made it solid with the original but improved greatly with the 360, which has forced both Sony and Nintendo to step their game up in the online service department (especially Sony which has now made PS online a wonderful service).

Sony nowadays is a life insurance company who happens to dabble in electronics. And wow, they find new ways to do things? Can you list them? Your last list was just a bunch of stuff other people created and Sony brought into their business.

Most of that is true but they are mainly minor innovations. Also, the Wii just got there first with console wifi (at least in Europe anyway). Shame only Nintendo kept backward compatibility though 

Didnt Nintendo do that first with the GameCube/Gameboy advance connector?

Nintendo- Gamecube/Gameboy advance connectivity (early foray into remote play?)
Motion controls- After the success of Wii everyone was trying it.
Stereoscopic 3D- glasses free on 3DS, and believe it or not im sure i read that Gamecube was capable of stereo 3D.
Touchscreen interface- Started with DS handheld, now on Wii U home console.
Miiverse- Nintendo gaming social networking site, one of Wii Us highlights. Able to post achievements, help fellow gamers, discuss games or show off cool artwork.
Wii fit board- started the whole fitness game craze, hugely popular.
Off tv play- Simple concept, but one of the best in gaming history in my opinion, so useful.
Super Mario Galaxy games- i had to add these as its not just hardware that can be innovative. These games just ooze innovation in every twist and turn. They are voted among the greatest games of all time for a reason.

and lastly- having a handle on the Gamecube :)

You do realize that what they do currently is nigh irrelevant to the context of the discussion, since this about past innovation. Life insurance carries them yes, but hardware is what they have done since the beginning. The only reason they are suffering on that front is because of Samsung and LG. Nintendo and Microsoft don't face nearly the same amount of competition, especially since MS makes most of its money from the private and buisness sectors.

No. You don't get to be subjective with this one. You can't call the Sony's innovations minor and praise Nintendo for being "revolutionary".  As a primarily hardware based company, most of their innovations are hardware focused,  and every single one of those have introduced many standards to the industry.

The idea of Sony playing it safe is laughable seeing how the company was nearly destroyed by the risks invovled with the PS3, the only console that significantly upgraded (new hardware) and had backwards compatibility at the time. The Cell was one of the most innovative flops of the decade.

Just because the Wii was successful doesn't mean it was very innovative, all it did was motion controls and ps2 esque backwards compatibility.

Microsoft and their online strategy was freaking huge with the original Xbox.
I played the DreamCast, but this is not a comparison.

Achievements

Games on Demand (XBLA / Indies)

HDD in a console

Video on Demand on a console