The question of backwards compatibility on the Playstation 3 doesn’t have a straightforward answer. There are some launch PS3 models that support backwards compatibility, but it is limited. The 20GB ( CECHB01 ), 60GB ( CECHA01 ) and the 80GB ( CECHE01 ) all support backwards compatibility with Playstation 2 games (These are the fat, 1st gen systems). This means that the slim PS3s do not support PS2 games. There are a few fat PS3 models that do not support backwards compatibility so it is best to check the model number first if you plan on buying one.
On the back of the box under the features, it will state whether the PlayStation 3 is backward compatible.
HD remakes are the way that Sony plan on allowing us to play PS2 games on the PS3. In the past few years there have been a lot of PS2 games released in digital form on the Playstation Store. These are different to HD remakes as they do not have upgraded visuals and any other additional changes from the original version of the game.