As this is specifically about Playstation I'll give exclusives or timed exclusives greater precedence.
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.