PS2 just had an absurd amount of games. And with a modded PS2, (as well as having more free time on my hands) the amount of games I was able to play back then is probably something I won't experience again.
It had just about any of the popular games you could imagine. But also many obscure games like RPGs for anime I was watching.
After PS2, I usually say PS1 because many of my favorite games are from that platform.
But I didn't have my own PS1, and I think PS4 may have brought me more fond memories.
My fav PS2 games in no particular order:
Metal Gear Solid 3
Kingdom Hearts 2
Resident Evil 4
Shadow Hearts 2