Do ps2 games play on a PS3?

Yes.

Only some of the games will work on some of the models of the PS3. Fewer of the games work on the new slim model than any other do to changes in both the hardware and software.

The above answer that was struck through was not correct. No new PS3 model in over 3 years could play PS2 games. Only 4 USB port PS3 models could play some and not all PS2 games