I can't give Nintendo credit for the analog stick. They weren't the first and many innovations came from elsewhere before they were incorporated by the "big three", such as the light gun.

Let's see.

Nintendo with the d-pad and shoulder buttons, two mainstays of gaming. They innovated portable gaming. Rumble, though it's vastly overrated. I believe the Power Glove was the first motion controller. Also, a lot of stuff that didn't go anywhere.

Sega with a controller you could actually hold without damaging your hands. They introduced internet play. First dual triggers? I'm not sure about that one.

Sony with DVD/media playback. Camera based motion controls. Also my favorite innovation, dual analog control.

Microsoft--mass storage?

Nintendo with the most, obviously. If we're talking most important, that would be closer.

Have you seen/played this? I was thinking of getting it myself - I found it used at a local shop on PS2. But it sounds like it's right up your alley :D

In fairness Sega came out with a controller in the late 80's/early 90's for the master system with shoulder buttons (and a modern analog stick for that matter)

Sony, because im being biased, lol!
Actually, i was gonna choose nintendo at first if i have to choose. But then i realized the Windows. I strongly believe that without Windows, PC gaming would not become as prominent as of today. And let's be real, PC gaming is king these days.
So Microsoft.

Wow, I did not know about that one.  Not only shoulder buttons but the first with four shoulder buttons.  I'd already given Sega credit for ergonomic design.  I don't think I can given them dual analog stick control, though this is close.  Dual sticks just offer more.

I might have to give Sega the win.

If we're talking more than games, it would be between MS and Sony, but game wise, I gotta give it to Ninten. They've done quite a bit for the industry. The game and watch, standard the d-pad, control set ups, the gameboy, the DS, motion control, there's so much they have done for the industry. They've pretty much set a lot of new standards once they came in with the NES.

Sony and MS have their own innovations, but before Sony and MS, there was Nintendo (and Sega) who largely helped shape gaming into what it is today.

That's definitely only one analog stick, but it's functionally the same as the N64's analog stick. I believe Sony gets credit for being the first to put two on.

But Nintendo's claim to fame is the shape of the directional pad, and rumble (where the system was taken directly from arcade games). That's pretty much it in terms of hardware innovation.

Nintendo, though I think that's mostly because they were around before a lot of things became standardized.

Oh, though I don't know why people give Nintendo the analog stick...

I like this answer. I came in here to say Nintendo, but the organized ecosystem that was brought with Xbox was extremely nice. Accounts were a nice way to have everything organized in the console, and achievements are an all-together fun addition.