Recommended PS3 games

[Made in China]

Metal Gear Solid 4: Guns of the Patriots.
3D Dot Game Heroes.
Heavy Rain.
Catherine.
Ico & Shadow of the Colossus Collection.
Metal Gear HD Collection.
Okami HD.
God of War HD.
Resident Evil 4 HD.
Ninja Gaiden Sigma.
Journey, flOw and flOwer.
Ni no Kuni: Wrath of the White Witch (Get the PSN version, disc version has freezing issues).
The Last of Us.
Kingdom Hearts 1.5 ReMix.
Kingdom Hearts 2.5 ReMix.
Metal Gear Solid V: The Phantom Pain (based on Ground Zeroes).
Persona 5.

Also on PC:
Metal Gear Solid: Revengance.
Metro: Last Light.
Far Cry 3 + Blood Dragon.
Deus Ex: Human Revolution.
BioShock Infinite.
Brutal Legend.
Dishonored.
Portal + Portal 2.
Bulletstorm.
Braid (PSN).

Based on your taste I would also recommend Burnout Paradise and the Call of Duty games, which I personally didn't like.
Also remember the PS3 also doubles as a PSX/PS2/PSP emulator. You practically can't run out of games with that huge library of games.

Edit(s): Added a bunch of games I didn't think about before, mainly PS2 HD remakes.