Anyway, if you are on the lookout like right now
There are some great platformers for the PS1 like the Spyro and Crash Bandicoot series. Both series still exists in PS2 library but some of them are quite broken, especially the time constraints for their development
PS2 still have a solid platformers though like the three kings such as Ratchet and Clank, Jak and Daxter and Sly Cooper
If you're a fan of stealth games or I guess a fan of "Tactical Espionage" action, then Metal Gear Solid series is for you! If you like hack and slash, then there's Devil May Cry and God of War (also the other underrated ones)
FPS? A bunch of old Call of Duty, but also there's Medal of Honor, Brothers in Arms, Darkwatch, Killzone, Rainbow Six and Timesplitters series, etc.
Or the even older classics like Doom, Duke Nukem and Quake. Horror? There's the big boys series like Resident Evil and Silent Hill
Racing? Well…A LOT! Like there's Wipeout, Need for Speed, Gran Turismo, NASCAR, Road Rash, Downhill Domination, Crash Team Racing, Midnight Club, etc.
A lot to choose from, but pick the genre you love and enjoy