InFamous, the Uncharted series, God Of War series depending on how bloody and violent you like your games, Street Fighter IV is good to pick up and put down if you were a fan of the old snes versions (the online community is die hard and very good so, fair warning), the Lego games, and I'm sure I'm missing a lot. But all can be had on the cheap, except Uncharted 3.
Heavy Rain was neat. Telltale have basically their entire recent library up on PSN. Both of the Batman games are awesome if you haven't played them already. The Pixeljunk games are wonderful. You can get Uncharted 1 and 2 in a combo pack for like $40. I guess it depends on what kinds of games you like. You'll likely have more games than time before too long, regardless.
I'll go ahead and recommend Catherine, even though it's kind of a weird game that is definitely not going to be up everyone's alley. It's about a guy's relationship problems. There are interactive story sequences inter-cut with puzzle levels. The puzzles are super creepy and atmospheric, and hard as hell with a steep learning curve. Beating them is really satisfying, though, and the whole production is top-notch, with great voice acting. I think there may be a demo you can check out.
As a late-to-the-PS3-party'er myself, these days I'm loving Red Dead Redemption. Gameplay's easy to pick up, stellar voice acting. Prototype was also very fun and nearly became my favorite sandbox game after Spider-Man 2 (nearly).
My side is the side of love, peace and submachine guns.
Originally posted by ScottyflamingoYou can get a lot of great games cheap since you are new to PS3. I would recommend Infamous, Arkham Asylum, Fallout 3/New Vegas and Uncharted. All of those can be found for under $30 a piece.
You could also download some PSN games. I like Flower and Zen Pinball.
To steal from DEAN: What worked: Rikimaru and Ayame: They both rock, and Ayame's a cutie that will slit your throat at a moment's notice. Each has a different story, even though the areas are the same. Also cool about Ayame: