There are actually tons of great PS3 games to play on the system. As a matter of fact, I could probably write down more than 20 of must play titles without even thinking twice about it. I will not though, and since there are already many titles that have been mentioned before my post, I will add Ni No Kuni. It is an awesome JRPG with incredible graphics and an amazing story.
The art style is phenomenal, it is just like watching an anime.
Also, this was not mentioned either, Demon's Souls. Excellent game. Immersive and tough as nails. Way harder than Dark Souls. Graphically, it may seem a bit rough nowadays, still it is far from ugly. Totally recommended.
There are still loads of games available and still being developed for the ps3. With the price of the console now coming down a fair bit aswell thanks to the release of the ps4, now is probably a good time to buy if your on a budget or just want a console to have a bit of fun with.
There's life in the old dog yet, as they say...
Uncharted 1-3: It is a action-adventure game. You play Nathan Drake who is suppose to be a descendant of Francis Drake, who seeks out lost treasures like El Dorado, Shangri-La and the lost city of Iram of the Pillars. As Drake you jump, climb, sprint, swim, scale narrow edges and wall-faces. It's one of my favorite games.
The Last of Us: Third-person survival horror action game. It is set in a post-apocalyptic US that tells the story of Joel and Ellie. Throughout the game Joel and Ellie work together on a westward journey across the US to find a possible cure for the plague that has wiped out the human race. By far one of the best, if not THE best game I have ever played.
Heavy Rain: This game is more of an interactive movie than it is a video game. It is a psychological thriller, where you play 4 different character in the search for the Origami Killer. Ethan Mars, the father of the kidnapped son of the Origami Killer, Madison Page, a journalist, Norman Jayden, an FBI agent and Scott Shelby, a private eye. All different characters that do not know each other but are all connected.
You've got loads of good games out atm.
For your 1st person Shooters, you've got the Call of Duty series. Black Ops and Modern Warfare 2. I personally prefer MW2 but that's because I'm a sniper and the snipers on Blacks Ops suck.
Then you've got the post-apocalyptic RPGs, like Fallout: New Vegas, Fallout 3 and Borderlands.
If you're looking for a fun little game, try Little Big Planet and Little Big Planet 2, or EyePet.
Other than that, you've got Assassins Creed: Brotherhood.
They're the best games out at the moment I think, but I know that there are some pretty good games out soon, so just keep your eyes open.