This is one of those questions that the answer is going to be very biased per person. Most of us have a certain timeline where we got into gaming and that's normally about the time we're going to see as the best gaming generation. If you look back, every few years whenever the new gen consoles are released. I'd say the best time is when the competition started to heat up. I started really gaming with Sega Genesis/SNES/TurboGrafx-16/Neo-Geo. Right after that is when the the PlayStation, N64, and Sega Saturn were released. I think that's when competition really picked up and the console wars started.
My vote would go to the 6th gen as gf78 mentioned. The 128-bit era gave us the PS2, Xbox, GameCube, and the Sega Saturn was still a legitimate machine. That's when I really started seeing competition between the companies and them jockeying for games exclusives. Before, it was primarily developers releasing games per console as they were paid. Seems like, at this time, is when bidding wars started for developer's services.
I think any gens 4th, and on, could all be argued to be the best ones to be alive during.