Please give me your opinions. Who brought the most innovations in the console market?
I'm not that well informed that's why I made this thread. What I mean is, which company added something that's now basic or is going to be basic? 

For example motion sensing, blue-ray, 3D. online gaming, remote play, giving indies support and so much more?

microsoft.

because they brought the online infrastructure... and Achievements.

Not that I like those games, the pay for online infrastructure, or achievements.

I don't, though I've come around to achievements.

The motion controls of wii are close, but that's heavily dieing now.

Microsoft - the driving force of online gaming in home consoles

Nintendo, for introducing new control interfaces.

Microsoft for making online gaming on consoles relevant! (  only if all the annoying kids would have stayed away... Oh well.)

Nintendo with the Wii ... like it or not, it definitely disrupted the marketplace and changed how people viewed video games. XBox 360/PS3 honestly just were straight forward iterations on the PS2/XBox, which isn't a bad thing, but they basically were just the next natural step.

XBox Live and Playstation Online was already well underway 10 years ago, so it can't really even be that. 

I'd say Nintendo. Even if the Wii died out, it was more innovative than anything Sony and MS had.

Sega started online.

Sony.
Started developing and even launched motion controls for consoles since PS2.
Started the greatest subscription based 'rental service' on console.
Brought the most F2P and MMO games to consoles..
Created the most new AAA IP's
Developing VR technology for a long time.
Allowed other OS option (until the hackers got the better of it)

and ofcourse, as OP states, they helped develop the blu-ray format and 3D and bring it to gaming, did remote play first with PSP and PS3.

Definately MS since they created the first, truly functional online community (yes, Sega was first on Saturn and Dreamcast but even I find it crap :)), introducing achievements, probably making the indie scene as big as it is now, introducing the best controller of all time and also introducing true, controller free motion controls.

Nintendo.
They didn't do always the best job but the most innovative like the Wii. It always felt like Sony and MS were doing the same things than the other two did but tried to become better. That's not bad but not innovative.