Facebook APIs don’t expose email addresses of users and hence none of the Facebook apps can provide you with the actual contact data of your friends. There’s however a simple (and perfectly legal) workaround that can help you easily download all your friends email addresses from Facebook’s walled garden.
The trick, as you can see in the video, is actually quite simple.
Go to address.yahoo.com and click the Facebook icon. A login dialog should pop-up, just sign-in with your Facebook credentials and within seconds, you entire Facebook address book will be available inside your Yahoo Mail Account. Once the import is done, click this link to download a CSV file with the email addresses of all your Facebook contacts to your desktop.
You can then import the CSV file into Gmail Contacts, LinkedIn, your phone address book or any of the social sites where you want to connect with your existing Facebook circle.
Update: If Yahoo! is unable to import your Facebook Address book, open your Facebook page and choose “Application Settings” under Account. Next remove the “Yahoo! Contact Importer” application from your Facebook profile and try the steps mentioned in the video again.
Source: Digital Inspiration