As this is specifically about Playstation I'll give exclusives or timed exclusives greater precedence.
PS1: FFVII
This game had an undeniably huge impact on the generation, introduced jRPGs to Europe, popularized them in the West and is still influencing Square-Enix even today.
Honourable mentions: Metal Gear Solid
PS2: GTA: San Andreas
This was the perfection of the GTA formula for the gen. So much to do, three distinct cities, loads of fun vehicles and a great story to boot.
Honourable mentions: Final Fantasy X, God of War 2, Shadow of the Colossus
PS3: Uncharted 2
This exclusive pretty much the main reason to own the console. A great combo of platforming, shooting and a bit of stealth thrown in for good measure. A cast with a chemistry that is rare to find in gaming and you have a brilliant experience that defines the console.
Honourable mentions: Deus Ex: Human Revolution, God of War 3, Oblivion, Skyrim
PS4 (so far): Uncharted 4, although Witcher 3 is up there but plays better on PC.