extract Apple ID's password from mavericks keychain? First of all i need to know if mail's passwords stored in keychain or not ?
If yes .. how to extract passwords from keychain especially [APPLE ID] ?
That's it
Open up Keychain Access, located in /Applications/Utilities/.  A list of all your stored credentials are listed in categories on the left.  I typically search for a credential by either the application it is associated with, or by the username.  



Double click on the credential you desire to obtain the password for.  A window pops up and there is a check box towards the bottom to Show the Password.  Check the box, you'll be required to type in admin credentials, and it'll show you the password it has saved.  



These instructions can also be found here