PS1:
Final Fantasy IX - Doesn't even need an introduction.
Bugs Bunny Lost in time - I had SO MUCH fun with this game. I was literally crazed for a weeks.
Crash Bandicoot 3 - WARPED! - Loved it to bits. Extremely enjoyable, more than its prequels.
Tekken 3 - It started in Tekken 2 for me...but 3 I remember the fondest.
PS2:
Ace Combat V - The unsung war - Currently and for a long time one of my favorite games.
Legacy of Kain - Soul Reaver 2 - Raziel...come back...I miss you.
Jak & Daxter - My favorite 3D platformer by far.
Kingdom Hearts - I still get shivers down my back remembering the awesome battle with Sephiroth and the elation of victory.
Primal - Never forget that a passion project game can and will surpass many higher profile ones.
Project Zero - The definitive survival horror game.
God of War - The original bad ass god slayer.
PSP:
God of War - Ghost of Sparta - One of the best God of War games there are. I'd honestly rate it as high as the first one.
The impossible game - I have no shame, I love this thing.
EMULATORS!
PS3:
Demon's Souls - FANTASTIC! I called it from the very first trailer and they've nailed my expectations to the wall and destroyed them.
Red Dead Redemption - I enjoyed it a LOT more than I ever thought I would.
Flower - Amazed me.
Resistance - Fall of Man - Good transition shooter, from the classic formula to the modern.
inFamous 2 - Loved it to bits, from start to end.
And many more on the PS3 front. There were a lot of great games this gen and it's hard to pick favorites.
