PS1: i dunno about this. it's a tie between crash bandicoot 3 and spyro 3. both excellent platformers.
PS2: this is a tough one. there were so many great games. i think Final Fantasy XII just because it was the game i played the most. and it was the game that made me love rpgs. honorable mentions: Staw Wars Battlefront 2, Ratchet and clank up your arsenal, gta san andreas, the sly cooper games. kingdom hearts II, Jak and daxter 1 and 3, and Final Fantasy X.
PS3: Ratchet and Clank Future A Crack In Time. the best R&C IMO. honorable mentions:
GTA V, Ni No Kuni, the elder scrolls oblivion and skyrim, littlebigplanet 2, the last of us, uncharted 2, god of war 3.
PSP: Gta Liberty city stories. honorable mentions: Ratchet and clank size matters, secret agent clank, Crisis Core:FF7, and Patapon 2.
PS4: not sure yet. there are some games i haven't played yet that could go here.