Commodore Amiga, 1985

Okay, this isn't strictly a console, it's a home computer, but if you owned an Amiga in the late-eighties or early nineties you owned one of the best games machines on the planet. This was the glory era of Britsoft when idiosyncratic UK studios like Bitmap Brothers (Speedball 2, Chaos Engine), Team 17 (Worms), Bullfrog (Syndicate) and Sensible Software (Cannon Fodder, Sensible Soccer) were in their pomp. It's also where a lot of technically gifted European studios like Guerrilla and Housemarque originated, courtesy of the 'demo scene', where coders, artists, and musicians competed to wring the absolute most out of the Amiga hardware. 

Sega Mega Drive, 1988

As the first major 16bit console, the Mega Drive was a massive success in the US and Europe, thanks to its combination of fantastic arcade conversions and authentic (for the time) sports simulations. It was the golden age of the scrolling action game, with titles like Streets of Rage, Altered Beast, and Mickey Mouse: Castle of Illusion typifying the genre, while EA came into its own producing the Fifa, NHL, and NBA simulations. There were also wonderful RPGs like Phantasy Star and Shining Force, as well as compelling blasters such as Gunstar Heroes, Truxton, and Contra: Hard Corps, all filled with colour and energy. And of course, there was Sonic the Hedgehog, his first three adventures still as astonishingly fast and vibrant as they were 20 years ago.

Super Nintendo Entertainment System, 1990

Some call Nintendo's 16bit machine the greatest games console of all time, and it's difficult to disagree. It was technically superior to the Mega Drive with more colours and clever sprite rotation/scaling hardware and it has a truly vast software catalog. Indeed, from 1990 to 1996, the system saw some of the most iconic series' of all time, from Final Fantasy to Street Fighter, with Nintendo wringing the most out of its exclusivity deals with Japanese developers. And of course, there were homegrown classics like Super Mario Kart, Super Metroid, and F-Zero, as well as the wonderful Donkey Kong Country titles from the first-party studio, Rare. And basically, if you want to understand the history of the JRPG genre, this is where to come and gorge yourself: Chrono Trigger, Zelda, Secret of Mana, Final Fantasy III... the list is endless.