Wow, I've been wanting to share my favorites for so long, I'm only 14 but here are my favorites:
Metal Gear Solid
Breath Of Fire 4
Final Fantasy 9
Hogs Of War
Worms Armageddon
Grand Theft Auto 2
Destruction Derby
Demolition Racer
Soul Reaver
Tomb Raider 3
Oddworld: Abe's Oddysee
Croc
Crash Bandicoot
Syphon Filter
I still occasionally play Hogs of War and Metal Gear Solid today, Hogs of War never had a sequel which Im quite sad about, because Im sure it would be so much better in HD to help you with your aiming, I hated it on PC though. Demolition Racer is probably one of the best destruction racing games ever, the graphics werent bad for the time, and your car actually got mashed up in different positions, unlike some racing games still today. Grand Theft Auto 2 was made alot better by 3, and then Vice City, SA and 4, but I think Vice City is the best of the series, if it wasn't for its horrible lack of physics. And to be honest, Just a few weeks ago I was playing Abe's Oddysee for about 2 hours a day. Croc is something like a family favourite, my Uncle that is only 3 years older than me had some good games on PS1, Croc and Syphon Filter being 2.
Breath Of Fire 4 seems to be a very rare game that my grandad bought for me in about 2000, and I could probably say I like it more than Final Fantasy 9, which is also a very good game by the way. Crash Bandicoot is extremely well known, and just the other day I bought it on PS3 (Arcade game from the PSN store)
That's all I can say, try and write if you like any of these games
EDIT: I also want to say that Tekken was and still is an all time favorite
