If you liked Final Fantasy VII, then I recommend Dirge of Cerberus. Great follow up that takes a Devil May Cry approach to action, with rpg elements.
The Dragonball Z Budokai and Tenkaichi Budokai games are good fun too, though I'm a bit of a biased person to recommend those in all honesty. If you like Dragonball, and you like fighting games, try them. Budokai 3 and Tenkaichi 3 I most definitely recommend.
The Kingdom Hearts games are must plays. The juxtaposition of Square-Enix characters/environments in a slightly angsty narrative, combined with the happy feel good (and yet still dramatic) Disney worlds, along with a good solid action RPG battle system, make for an extremely epic experience.
Metal Gear Solid 3 is an absolute must. As much as I love Sons of Liberty, it doesn't even compare to Snake Eater. I wont spoil the story for you, but in regards to gameplay the camouflage system really adds to the stealth gameplay, just try it!
If you see SEGA Classics Collection about then it's worth getting. It includes fun remakes of Golden Axe, Outrun, Space Harrier, Virtua Racing, and more, all with enhanced graphics. Worth a play.
No Playstation library is complete without a Wipeout game. Wipeout Fusion... get it.
I'll leave a list of some more, can't elaborate without going overboard on the length of the post.
Timesplitters trilogy, Tekken Tag/4/5, Mortal Kombat Armageddon, Gitaroo Man, Jak trilogy, Devil May Cry, Soul Calibur II/III, Zone of the Enders 1/2, WWE Crush Hour, Gran Turismo 4.