Overall, I'd say Gen 7; we started out with essentially just HD versions of PS2 games, and ended with things that really pushed the boundary of graphics, story, and gameplay. And there was that whole motion control thing that I think in retrospect most of us would rather forget had ever happened, but was still emblematic of a generation where it really felt like the industry was trying new things before going in a much safer direction from Gen 8 onwards.

That said, Gen 3 is a very close runner-up. Compare the graphics in the first Super Mario Bros to something like Castlevania III, and it's staggering to think they come from the same console.

Gen 7, but only for PS3/Xbox360. Not including the Wii.

I don't know if there'll ever be another significant gen like that ever again.

I actually really liked the motion controls on Wii when they were well executed, which was something that did improve a lot over the course of the gen both with devs figuring out more optimal uses and the introduction of motion plus in 2009.

Wii Sports Resort was a big leap over Wii Sports 1 for instance, while FPS controls improved hugely from early efforts like COD3 and Red Steel 1 to later efforts.

I still like them, they paved the way for VR to emerge on consoles. PS3 move controllers with PSVR1 worked great. 

There was also the Balance board, great piece of tech, simple durable and perfect for snow boarding games.

I am also gonna go with the seventh gen (although I acknowledge there is a good case to be made for both the third and fourth).
We went from Call of Duty 2, which looked good for sure, but we ended up with stuff like Assassin’s Creed Black Flag, GTA V, The Last of Us, Rise of the Tomb Raider, games that don’t look all that different from what we are still playing.
But also on aspects besides the graphics. In the start games ran off discs, by 2013 they could run off the hard drive for improved performance. At launch we could buy tiny games on the online store fronts, by the end you could buy any game that way.
For better or worse we saw the rise of DLC and games as a service.
We certainly also saw a huge jump in alternative ways to control games, the Wiimote was revolutionary from the start, but Motion+, PS Move and Kinect were certainly significant jumps.

Was thinking the 6th gen but looking back games early games still looked about as good as later ones even if some studios made large improvements.

The arguments for gen 7 has won me over at least on PS3 that was difficult to develop for so it took the generation to harness the full power. Not as large improvemts on 360 and Wii.

The cartridge based generations had a big advantage over the disk-based systems. New chips with improved capabilities could be added into the games themselves, almost like having a pro model of a modern console today.

Game design wise I still think the 6th generation had its moments, more so as experiments and not necessary improvements. While on NES games sort of got better all around, the first games look like they belonged on an Atari 2600 and the later like they could be for Genesis or SNES.

The PS3 version didn't get enough praise. It was sad to see the 7th gen end just when some devs had really cracked the PS3.

I would argue 360 saw enormous progress graphically; over the course of its life we went from this:

To this:

That is a substantial graphical improvement, I agree. 

I simply do not have as much experience when it comes to Microsoft's systems. Never owned (or ever saw a reason to own) any version of any Xbox.