Your (or in some cases you have multiple) email by default, is visible to all your friends through the info tab on your Facebook profile.
In order to hide the email go to: privacy settings, contact information. Scroll through the settings and the right of the mail you want to hide, click on the pull down menu.
Among the various options available choose "Custom". This opens a dialog box to set custom privacy. Select "Only me" which will hide the e-mail from everyone, or choose" Friends Only "and type the names or lists of friends who want to hide it from.