Hard to believe it's already been 25 years! I think I was introduced to PlayStation around 1999 when my cousin gave my oldest sister his PS1 and games since he had gotten the Dreamcast. It was one of the early model PS1s (the ones that had an actual composite connection) so the discs wouldn't want to spin properly unless it was on its side.
PS1: Mega Man X4- I love just plowing through this game. It doesn't have any weird gimmicks like the other X games (besides X1) that bog things down. Other than X4, I like Dragon Warrior VII, Mega Man 8/X6, Spyro 1, Zoop, and Wipeout 3.
PS2- Katamari Damacy- Along with Picross, this is one of my favorite chill games. Great music and such a simple fun idea. Other games I enjoyed were Sly 1/2, Dragon Quest VIII, Battle for Bikkini Bottom, Jak and Daxter, Hit & Run, SSX Tricky, and Kingdom Hearts II.
PS3- I don't really have a favorite for PS3 since I didn't get one until like 2014 and haven't played a game yet I'd call my favorite on the system. I did enjoy Sly 4, Puppeteer, Sonic '06, Metal Gear Rising, and Persona 5 though.
PS4- It's hard to pick just one, but between Dragon Quest XI and Owlboy, I suppose I'll go with Owlboy since I enjoyed the extra stuff the Switch version of DQXI added. Owlboy was a surprise for me. It looked like a fun 2D platformer adventure game from trailers and little bits of gameplay I saw, but I found myself relating to the main character Otis, liking many of the main/side characters, and in general, found the game to be a fun experience from beginning to end. Besides DQXI and Owlboy, I had fun playing Sonic Forces, Sonic Mania Plus, Mega Man 11, Team Sonic Racing, and Yakuza 0.