Unlock Original Prince of Persia Level 1 in 3D:
Start a New Game and stay on the balcony. Press L3 then press X, Square, Triangle, Circle, Triangle, X, Square, Circle. 

Prince of Persia Passwords:
KIEJSC Level 2 
VNNNPC Level 3 
IYVPTC Level 4 
RWSWWC Level 5 
GONWUC Level 6 
DEFNUC Level 7 
SVZMSC Level 8 
DBJRPC Level 9
MZFYSC Level 10 
BRAYQC Level 11 
UUGTPC Level 12
LRARUC Battle with Jafar 

Unlock the Original Prince of Persia:
Complete the game and Prince of Persia 1 will be playable in the extra options menu. 

Unlock Prince of Persia 2:
When you receive a new sword around 33% through the game, continue on until you break a wall and the Prince says, ''It's said they built this palace on the ruins of another...'' Once you cross the next room, you will find a rotatable switch. Directly behind this switch is a breakable wall, although it doesn't appear to be. If you hit it three times, you will find another room and you will receive a message informing you that Prince of Persia is now unlocked. 

Note: You can also rotate that switch until it points to the new room and it will open a gate that allows you to play Prince of Persia 2 right there without having to exit back to the Extra Features screen.