Feedburner does provide a very useful service, but sending subscribers directly to the Feedburner feed is a mistake that many bloggers (including myself until recently) commit. By sending subscribers directly to the Feedburner feed I mean placing an RSS link on your website that points to “http://feeds.feedburner.com/yourfeed”.
Why is this a mistake? Because on this way the readers will not be subscribing to your feed but rather to the Feedburber burned feed of your blog. This means that a third party is in control of the subscribers. Should Feedburner break down or decide to charge money for the service on the future you will lose the subscribers.
A simple solution for this problem is to make readers subscribe to your feed (i.e. http://www.domain.com/feed/) and redirect them to Feedburner. There are several ways to create the redirect.
If you already have a .htaccess file on your server you can simply add this code (it works with /feed/, if you use /rss/ you will need to edit it):
RewriteEngine On
RewriteCond %{HTTP_USER_AGENT} !feedburner [NC]
RewriteRule ^feed/?$ http://feeds.feedburner.com/yourfeed [R=302,L]
RewriteEngine Off
Alternatively you can use the Feedburner Replacement plugin that will redirect all your incoming feed requests from readers to the Feedburner feed.
Finally, if you do not want to redirect your readers but still want to access the Feedburner detailed statistics you can add this code to your feed file (i.e. rss.php or similar):
$feedburnerfeed="http://feeds.feedburner.com/yourfeed";
$ch = curl_init();
$useragent=$_SERVER['HTTP_USER_AGENT'];
curl_setopt($ch, CURLOPT_USERAGENT, $useragent);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
curl_setopt($ch, CURLOPT_URL, $feedburnerfeed);
$data = curl_exec($ch);
curl_close($ch);
Thanks Leo Paiva for the .htaccess tip and Mark Wielgus for the PHP code.
Update: The two redirect methods work only for people copying your feed address directly into their readers. If they click on the link, they will get redirected to Feedburner and they will end up subscribing to that feed. The PHP code method so far is the only way to retain 100% control of your subscribers.