Instructions
Update your PlayStation 3's firmware using the "System Update" feature in the main menu. Sony occasionally releases firmware updates for the PS3 that add compatibility for new types of media. For example, the PS3 could not read 3D Blu-ray discs until the October 2010 firmware update. With this update, the PS3 is now a fully compatible 3D Blu-ray player.
Check your disc to verify that it isn't scratched or dirty. The PlayStation 3 isn't a miracle worker -- just like with any optical disc drive, the PlayStation 3 isn't going to be able to read the data contained on a disc if the data side of the disc is scratched or full of dirt or dust. If the data side of your disc matches this description, you will have to either clean it (if it is dusty or dirty) or replace it entirely (in the case of deep scratches) to get your PlayStation 3 to read it.
Download the "PS2 System Data" from the PlayStation Store, accessible through the main menu of your PlayStation 3 console. If you're playing a game that required a hard disk drive attachment to be played on a PlayStation 2 (like Square Enix's "Final Fantasy XI", for example), you will first need to download and install the free "PS2 System Data" add-on from the PlayStation Store before the game can be read properly.