Before I had a console and I used to have to go to friends' houses to watch their SNES and Megadrive (Genesis), there was something magical about those 16-bit games with their trippy graphics and their MIDI soundtracks, a sort of magic that I still feel when I see a proper old school game of that age being played, or even when a soundtrack that is kinda reminiscent of that era is played somewhere.
Doom and Doom 2 on the PC came later, they properly immersed me 'cos a (fake-)3D shooter was quite a big deal back then. I used to still play them sometimes (along with Final Doom) when I had the PC before this one, 'cos it had a CD drive and this one doesn't. Quite liked the groovy music in them too (also MIDI files, but mostly a lot different to the SNES/MD tunes).
Ridge Racer in arcade form was awesomeness, I loved everything about it, from the utopian seaside sun-drenched setting and generally bright graphics, to the Japanese music (my first introduction to it I think), to the oversteery handling. I wasted a lot of money on it back in the day. Any time I see a RR cabinet (they do still exist, though they are quite rare now, not seen one in ages) I will still play it too, and be quite good! Knowing that the PS1 had an even better version, I knew I had to get into console gaming, so a PS1 was purchased (which arguably actually makes this my "most important" one. How shallow of me, a racing game with one and a half tracks!
).
FF7 though was the first proper bowl-me-over game I played. The PS1 was my first console so it probably helps that my introduction to owning my own console had the arrival of FF7 shortly afterwards to boost those nostalgia feelings. Unlike Ridge Racer, which was a game I knew and wanted, FF7 was something I didn't know much about, I just knew it had to be a big deal since it had TV adverts was back then. I played it without any expectations. Being new to gaming, it took a while to get used to the stats and materia junctionings, but the story and all the little extras immediately had my attention, and kept it for the next 60-odd hours. I replayed it countless times and actually still have the original double-hinged PS1 box version of the game. It will be worth a lot on ebay one day, but to be honest, it reminds me so much of a simpler and more innocent and just "fun" time of my life I may never get rid. Music was also top notch IMO, how many other games have an end-boss scene where the music has an orchestra actually singing the bad guy's name? Can't be many. When I see the opening scene on youtube, or even hear the intro theme, it gives me goosebumps, no shit. Don't know what that means since I'm not a woman, but some sort of emotional attachment is there. I will replay it again some day too. Have it on the PC from Steam, but it's not as much fun I don't think...
Special mention to Deus Ex too, I remember when we got our first PC (Doom was initially played on PCs that weren't mine) I bought Deus Ex soon after and was amazed by it most of the way through. I think I still had a PS1 at the time so Deux Ex was proper next-gen stuff back then.
I especially liked to wander about twatting people with that really sharp light blue sword that you ended up with. Decent story too I thought. And I think it featured Wan Chai before Shenmue 2 did!