Oh, great thread!
Let's see... When I was like 5, I'd go to the local arcade with my parents and there were only really old games like Galaxian and such. I really liked a monochrome football/soccer game that was played with these wheel-like things you rolled with your fingers - one for up-down movement and one for left-right... I think it was for 2 players only... Yet I spent some coins trying to score a few goals. Then, as the 90s started, they'd gradually upgrade the arcade machines and I enjoyed games like E-Swat and The Punisher by the time I was 12-13... There were several arcades around the town, I suppose they must've made decent money off kids like me. Meanwhile, I got an Atari 2600 at the age of 10. At that time, some other kids in Europe were playing SEGA Mega Drive... (I only got that when I was 15 and I'd saved up allowance for a few months.) The Atari had 128 games built-in and I played it a lot, some neighbour kids were coming over to play, too.
3 years later, I got a bootleg NES for Christmas, and soon enough I got a Captain Tsubasa II cartridge... Of course, by then I'd already beaten the game by renting NESes and a multi-game cart which also had TMNT3: The Manhattan Project on it from a local gaming club. But it was a pleasure to finally own it and play it as much as I wanted. Speaking of gaming clubs, many console clubs popped up around the town between 1994 and 1998. At first 8-bit NESes, but then mostly SEGA Mega Drives, later even PlayStations. They were really popular and kinda replaced the arcades. You could play there for a fee, or just rent the consoles and games. So many wonderful memories renting NESes and playing with my brother... Since it was 24-hour rental, we'd often wake up very early and go to play as much as we could before we had to return it... But by the turn of the millennium many kids had computers already, and that business died down. Back to my own NES, I also found games I really treasure to this day, like Dick Tracy and Little Ninja Brothers. And of course, the amazing Nekketsu games, easily the best NES series.
Like I mentioned, I got a Mega Drive when I was 15 and played that a lot, too. Funnily, I changed a few while the warranty was still up. I broke the first one tinkering while thinking there was something wrong with it because my FIFA saves kept getting erased (it was probably just a shitty battery). Then the next one had some issues restarting while playing Dune: The Battle for Arrakis - the first RTS game I ever played (and 2nd ever created). Another truly remarkable game I found on the Mega Drive is Uncharted Waters: New Horizons - a seafaring adventure RPG. You could be a trader, a pirate, whatever you wanted. You could just stray from your character's story (there were 6 characters to choose from, each with their own story to follow) and pillage the seas for years if you wanted... Really neat.
Then, in the last year of high school, I got a computer, and for a while I played PC games like Diablo II, FIFA 2001, Max Payne... I really played FIFA a lot for a year or so. Then my brother continued, it was the last big game he kept playing. Then, I discovered emulation and played the likes of Chrono Trigger and Final Fantasy VI. Then PlayStation ones like Chrono Cross, Castlevania: Symphony of the Night and Final Fantasy Tactics, later Xenogears. As for Final Fantasy VII, once we'd jumped past the dial-up internet and speed was sufficient to download it, I played the PC version, particularly the "Ultima edition" I found on some torrent site. That was some 7 years after it'd come out. Truly a timeless game. Final Fantasy Tactics was also great, and a bit later Xenogears really astonished me. I'd already started work when I played it, and I remember I kept thinking about the story, characters and what would happen next regularly on my way to work. That was amazing. No game has had such an impact on me so far, although the Metal Gear series come close.
More recently, I got a PS3, my first and probably last PlayStation console, in November 2008. I made sure to get the PS2-backwards compatible model, though it was obscenely expensive compared to the non-BC ones that had just come out. It was something like 30% more expensive. It's still working well... Getting close to that fated 10-year lifespan. Though it's not getting played much recently. I got a PS3 for Metal Gear Solid 3 and 4. I'd only played 1 and 2 beforehand, the PC versions. I really wanted to see Snake defeating the Patriots... Of course, upon playing MGS3 I'd realise Snake was but a poor man's Big Boss. I loved MGS4 and the conclusion it brought. Aside from that, I can't say PS3 brought many amazing games to me, though. I really liked Mirror's Edge and some older things like the Katamari games, ICO, Shadow of the Colossus, Final Fantasy X... The most memorable games of that period are actually the PS2 Xenosaga series - spiritual successor to Xenogears that couldn't quite match it, but came pretty close and I was delighted. Of course, I played two of those emulated on PC - only the second one had come out in Europe.
In autumn 2011 I also got a PSP which I played a lot while on the metro to work... I beat things like FF Type-0 and other PlayStation RPGs such as Grandia and Parasite Eve on it. Nowadays I'm mostly using it as a Captain Tsubasa II machine...
And here we are today... I have a child and I'm down to playing less than 10 games per year. But it's not so bad. As long as I can keep playing even a little, I'll be catching up on the great things I've missed. My hope for the future of gaming is close to zero. But there are lots of great things from the 90s and 00s that I still haven't played.