For real this time:

PS1 - Azure Dreams, Final Fantasy VII, Final Fantasy VIII, Lunar and Lunar 2, Wild Arms, Mega Man Legends 2, Mega Man X4, Breath of Fire III
PS2 - Time Splitters 2, Kingdom Hearts and Kingdom Hearts 2, Final Fantasy X, Dark Cloud

PS1/2: Tony Hawk Pro Skater

Of course I played a lot more PS1 and PS2 games than this, but those are the really memorable ones.

Final Fantasy 7-10, Grandia, Tony hawk pro skater 2, Shadow of the Colossus, Persona 4,Demons Souls, Dark Souls

your love for Flower is just too darn cute :)

Little Big Planet is pretty awesome. I sunk a shitload of time into that game, and will remember it always.

PS1:

Crash Bandicoot 1,2,3 and CTR
hercules
Spyro 1,2 and 3

PS3:

Uncharted 1 and 2
Heavy Rain
God of War 3
Flower
Resistance 1 and 2
Heavenly Sward
inFamous 1,2 and festival of blood
Trine
Assassin's Creed 2
Ratchet & Clank: A Crack in time
Dead Space

as for the PS2.. i kinda skipped most of that era unfortunately but i'm catching up with the HD releases :D

PSX - Valkyrie Profile, Xenogears, Chrono Cross
PS2 - Valkyrie Profile 2, Okami
PS3 - Valkyria Chronicles, Bayonetta

I forget Tekken 3 on psx... That was one of a game back then.

PS1: Gran Turismo 2
PS2: Final Fantasy X/X-2
PS3: Tales of Graces F
PSP: Kingdom Hearts Birth By Sleep
PS Vita: NA

I've never owned a Sony console until 2011.
But I remember having lots of fun playing Crash Bandicoot games at after-school daycare.
I had many memorable times playing Star Wars Battlefront II at my friends' houses.
The Uncharted series is one of my favorites on PS3. Same with Infamous
I really liked Heavy Rain, and I'm glad I got to play it early in my PS3 ownership.
Soon, The Last of Us will be added to the list of amazing Playstation games.

Recently I acquired Jak and Daxter Collection, Ratchet and Clank Collection, Killzone Trilogy, and God of War Saga, and I have the Sly Cooper collection on digital. So I'm ready to catch up on my PS exclusives.