WordPress Login not working with email address

Solution: 

If you don’t want to use a plugin, you can add the following to your functions.php file it will allow you to login with the username or email address:

// remove the default filter
remove_filter( 'authenticate', 'wp_authenticate_username_password', 20, 3 );
// add custom filter
add_filter( 'authenticate', 'fb_authenticate_username_password', 20, 3 );
function fb_authenticate_username_password( $user, $username, $password ) {

// If an email address is entered in the username box, 
// then look up the matching username and authenticate as per normal, using that.
if ( ! empty( $username ) )
    $user = get_user_by( 'email', $username );

if ( isset( $user->user_login, $user ) )
    $username = $user->user_login;

// using the username found when looking up via email
return wp_authenticate_username_password( NULL, $username, $password );
}

(The above was found here and I tested it and worked for me)