You definitely need to get Uncharted 2 ASAP.
You should also get Assassin's Creed 2 and if you like it AC: Brotherhood. The first AC game is fairly decent, but can also be quite tedious. So it's up to you if you get it or not. If you don't, I'd suggest you read a recap online or something like that (maybe watch a few YouTube videos).
One of my favourite (PS3) games ever is also Valkyria Chronicles. It's this interesting mix of strategy, FRP, and third person shooter. I can see how some people wouldn't like it, so you could always download the demo or read a few reviews before buying it.
The Ratchet & Clank games are also a lot of fun. As an alternative, you could also get the Sly Cooper collection (three games for the price of one). Oh and Just Cause 2 is also a VERY entertaining game.
If you like unrealistic racing games, you should get one of the Motorstorm games. Then you have the well known games like Gran Turismo 5, NHL11, Battlefield: Bad Company 2, all the Call of Duty games...
One game I also REALLY enjoyed was the 2008 Prince of Persia. Oh and Mass Effect 2, just like Uncharted 2 I really think every PS3 (and PC/360) owner should play ME2.