As best as I can remember, the Golden Age of gaming would have to be considered the mid-late 80s to about the mid 90s.
The games back then actually were "pop it in and play" (except for the ocassional cartridge blowing or alcohol swabbing...), and some of the most fun games I ever played were made during these years. Legend of Zelda(1,2 Link's Adventure, Link to the Past), Final Fantasy(1-4, not really counting 5 and 6...), Mortal Kombat, Sonic the Hedgehog, Killer Instinct, Street Fighter(back when it was still fun...), the list goes on.
Honestly, it was the golden age because you had all the older systems like Atari out of the picture. The games were largely being focused towards two platforms at any given time. Super Nintendo or Sega Genesis(Not counting Handhelds... Gameboy kind of dominated the market even despite its black and white screen versus the full color Game Gear). The market was more focused, and in a way less saturated by terrible games(albiet there were still many, but never anywhere near as bad as games like E.T. which were being pushed out prior to then... *Shudder*)
Once the clutter was gone, and people were able to know what to buy(I'm talking the misinformed parents here... They never kept up with the technology shifts), plus the reduced saturation in games, Studios were able to focus a little more on the quality of their games. Life was good, we played Super Mario Kart or Sonic 2, and we didn't comlain very much. Except when we saw Game Over...
Then Sony got into the game(pun not intended...) with their brand new 3D capable Playstation, Nintendo and Sega also made their new 3D systems, and the definition of "Good Games" started to shift away from "fun" and towards "pretty". Eventually, the whole market shifted so much that Sega just couldn't sustain with their failing sales of the Dreamcast(Even if it was a better system than the PS2 in my opinion...), and dropped out all together. The Titanic Two of the 90s(as I called them anyway) had been reduced to one, and now only Nintendo remains from that period. Entering into the PS2/Gamecube/XBOX era I would consider to be the beginning of the Silver Age(to borrow Comic book type ages...), and the PS3/Wii/XBOX 360 was the end of that, and now we're in a second Bronze Age(the first being those classic games/systems from the 70s-mid 80s), and everything is becoming saturated again to the point of near collapse.
Look at EA, or more recently with the AC:Unity debackle, Ubisoft. Games are being pushed out too fast now, their not being tested enough anymore, and everything has to look better and better always focusing more on the graphics now, but the gameplay itself which is what we use to play games for has become stale and less and less fun. Stories in recent games too are starting to suffer from this, Assassin's Creed was originally going to tell a specific story, but recent interviews reveal that the developers changed their minds and are now just going to make it all up as they go because it's their cash-cow equivelent of Call of Duty, which I don't even want to get started on the CoD franchise...
Mass Effect is another example where the story was "pancaked" on by the developers and in the end, it didn't matter what you did, the story basically ended the exact same way with only slight variations(after the DLC fix...).
Additionally, if you factor in the Mobile platforms(Android/iOS/Surface), the market is already so saturated with Flappy Bird and Angry Bird clones and game after game copying the other "sucessful" game in that genre, that it's becoming increasingly harder to sift through all the crap to actually find the good games. We are quite possibly walking the razor's edge border of another Gaming "Dark Age". The industry barely survived the last one by the way...
In fact, we're already seeing the effects given how numerous game studios, including Paragon Studios, have gone bankrupt or been shut down by their bank-rolling owners. It's hard to say how much of that is a reflection of the economy itself, but I would think for the most part if a game is doing well, the studio wouldn't just shut down out of the blue. Although, there are some games that end up bankrupting the studio that made them because of just how expensive they were to make(L.A. Noir I'm looking at you...), this is hardly becoming a standard in the industry... At least I hope not.
Still, it's not all bad. The developers who still actually take pride in their work have been able to produce some outstanding games recently(Granted I'm biased towards the Wii-U titles, such as Mario Kart 8, Hyrule Warriors, or the new Smash Bros. game...), so there are still some candles burning their brightest to keep us out of that "Dark", and some indie studios have been able to produce rather impressive titles that have done really well. I can't say for certain which way the market will tip in the end, but I would like to hope that we will not see a second crash.
TL;DR: The Golden Age was the NES/SNES/Genesis years.
P.S. Reading through my post, I kept reading it in a Mat Pat voice like this was some Game Theory episode... I've been watching his Youtube channel too much lately I think... If you haven't seen his channel before, you should totally check it out. Interesting theories on a whole slew of game-related topics...
Anyways, that's all just a theory. A History Theory... Yeah, no, I'm done...