At the title screen, press R2, R2, R2, L1, Triangle, L2, L2, L2, R1, Square.
Unlock Face Off Mode:
When you complete a championship in the Championship mode, the Face Off mode will be unlocked and you can race against other cars to unlock them. Keep completing championships and more face offs will be available.
Unlock Free Run Mode, Free Run Twin Mode & Credits:
Complete the entire game to unlock the Free Run mode, the Free Run Twin mode and the Credits option. The Free Run mode will allow you to race without any other vehicles on the road. The Free Run Twin mode is the same but two players can play it.