Facebook is the home of millions or I have to say billions of exciting applications which will bound the users to Facebook.
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To use these applications you have to grant them the permission of accessing the basic information of your account. Some of them also needs to know your email address.
If you want to avoid the sharing or accessing of your email address then you just have to click change button which will given in the details of request for permission of access.
You can see that as shown in image -
After clicking on change button select "An Anonymous email address" in place of "Facebook Contact Email".
You can see a trial in this image -
After doing this your email address will remain hidden from the developer of that application.
Would love to here from you...