For me it was definitely the Atari ST / Amiga 500 era, because they combined PC like functionality with dedicated gaming. The period saw a lot of interesting innovations, mouse controls, multi-player LAN stuff, demo scene, etc. The PC was exciting in this period too. Really, a lot of genres were new back then. Games like Populous were just something so incredibly new, in so many ways. Ditto for Sim City, or Civilisation. Whole genres were invented.
Of course, a bit part of it for me was that it was my first real era and I was in my mid-teens ... (I caught a bit of the Atari 800XL vs Commodore 64 era too which got me into this).
I think the coming console era has a lot of the same kind of potential though, with the Wii, PC, 360 and PS3 all strong platforms, online really coming into its own in the console space, cross-over options with very interesting handheld platforms, innovations in controls, small downloadable games, user creation tools and Linux installs possible on PS3, and so on and so forth.
Really looking forward to this gen!
I had an Atari ST and initially that machine was doing really well, because it was cheaper and pretty easy to develop for. But eventually as the Amiga came down in price it really took over, with far superior sound in games thanks through its better hardware and wonderful sample tracker software that made such efficient use of it. The Atari ST was great too, mind, and had a lot of unique things going for it. But eventually I even owned an Amiga for a short while (Amiga 600 HD), just so I could play all those great classics that I had been playing at friend's place before (Alien, Super Frog, Fantasy Pinball, etc.)
I think Populous 2 was my favorite game from the era, even if I didn't even play it that much. I played a lot of Geoff Crammond's F1 game on the Atari ST too. I also had an external Roland MT-32 synthesizer hooked up to it, which was supported by a lot of Sierra games on the Atari ST. Larry 3 had some amazing music for it back then, and sent wonderful little messages through the display at times as well, which was awesome. Then there was 16-player online Midi Maze, a 3d shooter, believe it or not, first version already back in the late 80s or very early nineties, even before Doom and Quake.
Shortly after this era, PC gaming dominated (3dfx for the win!), and then came the Playstation 1.
Ah, so many memories!