If this poll were asking which console/generation was the most influential, I'd have a really hard time answering it. Thankfully, it doesn't specifically ask that question - it just asks which I personally think is greatest.
With that in mind, I'm going to go with SNES/Generation 4. My choice has nothing to do with innovations or later influence, as it's entirely based upon nostalgia and personal fun. I've owned at least one console from every generation at one point or another, but the SNES was the first one that I really felt attached to. Classics like Donkey Kong Country, Earthbound, Zombies Ate My Neighbors, and of course, UN Squadron really solidified my interest in gaming. Also, I have fond memories of playing SNES with my parents.
So yeah... SNES, my personal greatest console. Maybe not the most influential to gaming in general, but probably the most influential to me as a gamer.