If you are not running your feed through Feedburner, you are missing out on great information to help you cater your content to your audience.
I used to be a big advocate of not using Feedburner when RSS news feeds first became important several years ago. I did not want to lose my domain branding on my feed by having it be wrapped by Feedburner.
But now, I recommend that you use Feedburner as feed stats at the PRO level are free now that Feedburner has been purchased by Google. It’s easy to create a free account. You simply enter in the URL for your blog in Feedburner and it creates a new feed URL for you. If you are using Blogger, you enter this new feed address in the feed tab of the settings. For WordPress users it is more complicated. Typically I will hard code the feed into the meta tags, but you may actually now be able to find a plug-in that will allow you to install the Feedburner feed automatically from one of my last plug-in searches. I haven’t checked it out yet, so if you have, leave me a comment.
I monitor my Feedburner stats to see what is happening in regards to broad subscribership. Remember however, Feedburner only provides stats on your RSS or Atom feed. It does not provide page views when people visit your blog using their browser or a link from your website. So, you will still need to review stats like Google Analytics or Urchin for the full picture of the popularity of your blog.
It is important to understand that according to industry reports that still only 7% of all readers are reading blogs via feeds so your real traffic will still be coming in via a browser. So make sure you have regular web stats enabled for your blog to track all of your traffic.