Wordpress login to download uploaded files

dl-file.php

<?php
/*
 * dl-file.php
 *
 * Protect uploaded files with login.
 * 
 * @link http://wordpress.stackexchange.com/questions/37144/protect-wordpress-uploads-if-user-is-not-logged-in
 * 
 * @author hakre <http://hakre.wordpress.com/>
 * @license GPL-3.0+
 * @registry SPDX
 */

require_once('wp-load.php');

is_user_logged_in() ||  auth_redirect();

list($basedir) = array_values(array_intersect_key(wp_upload_dir(), array('basedir' => 1)))+array(NULL);

$file =  rtrim($basedir,'/').'/'.str_replace('..', '', isset($_GET[ 'file' ])?$_GET[ 'file' ]:'');
if (!$basedir || !is_file($file)) {
	status_header(404);
	die('404 &#8212; File not found.');
}

$mime = wp_check_filetype($file);
if( false === $mime[ 'type' ] && function_exists( 'mime_content_type' ) )
	$mime[ 'type' ] = mime_content_type( $file );

if( $mime[ 'type' ] )
	$mimetype = $mime[ 'type' ];
else
	$mimetype = 'image/' . substr( $file, strrpos( $file, '.' ) + 1 );

header( 'Content-Type: ' . $mimetype ); // always send this
if ( false === strpos( $_SERVER['SERVER_SOFTWARE'], 'Microsoft-IIS' ) )
	header( 'Content-Length: ' . filesize( $file ) );

$last_modified = gmdate( 'D, d M Y H:i:s', filemtime( $file ) );
$etag = '"' . md5( $last_modified ) . '"';
header( "Last-Modified: $last_modified GMT" );
header( 'ETag: ' . $etag );
header( 'Expires: ' . gmdate( 'D, d M Y H:i:s', time() + 100000000 ) . ' GMT' );

// Support for Conditional GET
$client_etag = isset( $_SERVER['HTTP_IF_NONE_MATCH'] ) ? stripslashes( $_SERVER['HTTP_IF_NONE_MATCH'] ) : false;

if( ! isset( $_SERVER['HTTP_IF_MODIFIED_SINCE'] ) )
	$_SERVER['HTTP_IF_MODIFIED_SINCE'] = false;

$client_last_modified = trim( $_SERVER['HTTP_IF_MODIFIED_SINCE'] );
// If string is empty, return 0. If not, attempt to parse into a timestamp
$client_modified_timestamp = $client_last_modified ? strtotime( $client_last_modified ) : 0;

// Make a timestamp for our most recent modification...
$modified_timestamp = strtotime($last_modified);

if ( ( $client_last_modified && $client_etag )
	? ( ( $client_modified_timestamp >= $modified_timestamp) && ( $client_etag == $etag ) )
	: ( ( $client_modified_timestamp >= $modified_timestamp) || ( $client_etag == $etag ) )
	) {
	status_header( 304 );
	exit;
}

// If we made it this far, just serve the file
readfile( $file );

If you're a PHP/.htaccess noob like me, and you're trying to implement this, please read before attempting to implement. It may save you some head banging and throat punching...

dl-file.php file goes in your public_html directory (the same place as your wp-config.php files and such)
Add the additional lines posted by stewartadam for new version of WordPress in dl-file.php
The .htaccess file you should be modifying is the one in the above directory.
This solution locks EVERYTHING in your wp-content/uploads directory. This was the issue I was facing and was having misunderstandings with.
I'd imagine most people don't want their entire wp-content/uploads directory to be locked. Header images, images in public posts, etc. are all stored in this wp-content/uploads directory by default. If you're wanting to have a dedicated "membersonly" folder inside your wp-content/uploads directory, leaving alone existing content that you don't want to restrict, you'll have to make some modifications to your .htaccess file.

Here's my .htaccess:

# Use PHP5.4 as default
AddHandler application/x-httpd-php54 .php

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /~MyWebsiteFolder/
RewriteRule ^index\.php$ - [L]

# BEGIN THIS DL-FILE.PHP ADDITION
RewriteCond %{REQUEST_URI} ^.*wp-content/uploads/membersonly/.*
RewriteRule ^wp-content/uploads/(membersonly/.*)$ dl-file.php?file=$1 [QSA,L]
# END THIS DL-FILE.PHP ADDITION

RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /~MyWebsiteFolder/index.php [L]
</IfModule>

# END WordPress

Options -Indexes

APACHE

RewriteCond %{REQUEST_URI} ^.*wp-content/uploads/restricted/.*
RewriteRule ^wp-content/uploads/(restricted/.*)$ dl-file.php?file=$1 [QSA,L]

For NGINX

location ~* /(?:uploads|files)/* {
    rewrite /wp-content/uploads/(.*)$ /dl-file.php?file=$1;
}

Options -Indexes to prevent directory browsing.
The location is important here. It must come before the two lines of RewriteCond and one line of RewriteRule. These three lines send all file requests to index.php, which is not what we want. Putting THIS DL-FILE.PHP ADDITION before those three lines ensures dl-file.php is getting called when it should be.
In the RewriteRule ^wp-content/uploads/(membersonly/.*)$ line, it's important if you want a specific directory to be protected that you encapsulate it in parenthesis like that. What is in parenthesis gets sent to dl-file.php. This basically says, any calls to anything inside membersonly get sent to dl-file.php, with the 'file' variable being set to membersonly/SomeFile.
Hopefully this helps at least one person save a few unnecessary hours of anger and frustration...