Step 1. Enter Service Mode.
Step 2. Downgrade your PS3 System to System Software Version 2.50 (this is the one that supports more PS2 gaming).
TUT here:You must login or register to view this content. (Instead of downgrading to 3.41, downgrade to 2.50)
Step 3. After downgrading don't get out of service mode.
Step 4. Uncheck Game-auto start in System Settings.
Step 5. Insert your PS2 disk cd/dvd on PS3.
Step 6. Load it and do not press the PS Button while playing otherwise it will crash.
Tested on a CECHP01 Console. The one game that would play exactly like in a PS2 was Twisted Metal Black.
Note: DO NOT TRY THIS ON A PS3 SLIM IT BRICKS! (But can be recovered while in service mode)
This is a good thread though however it's way to risky and I don't think many people will be happy downgrading to 2.50 as they will be losing quite a few features.