The original launch 60gb and 20gb models could play PS2 games. Then the old 80gb (MGS4 bundle ones) could also play PS2 games through emulation, but now those 80gb models don't exist and don't come with backwards compatibility.
Just to clarify though, all PS3 models can play PS1 games no matter what. Also, just recently it's been discovered that Sony has filed a patent which would allow all PS3's to emulate PS2 discs through the cell processors.
Kotaku - Sony Patents Method To Emulate PS2 On PS3 - PS3