The Playstation 3 has some backwards compatibility with the Playstation 2. The level of compatibility varies, depending on the model type and number of Playstation 3 and the version of the firmware it is running.
Not all Playstation 2 games can be played on a Playstation 3, but there are hundreds that can potentially work. Official backwards compatibility (added by design by Sony) is only available with the 20 GB, 60 GB and older versions of the 80 GB systems. Unofficial compatibility can be added to the other models by installing an aftermarket chip, though this is not supported by Sony and voids the system's warranty. Official compatibility for any individual game can be checked at Sony's website with a search tool.