As I've mentioned previously one of the many reasons I decided to "go it alone" with my blog and move from blogs.borland.com was the lack of site usage statistics including usage of my $g(RSS feed). Of course, I could provide only excerpts in my feed forcing readers to click through the site but I personally won't subscribe to non-full text feeds so I can't really expect that of anyone reading my blog.
That's where FeedBurner comes in. When $g(Scott Hanselman) mentioned it here I headed over to check it out and now they host my RSS feed providing me with all sort of stats on it's usage. They even provide web site services for example, I can place what they call a chicklet like this 
on my blog that displays the number of current subscribers for that day. I can also get information on:
- Which feed readers are used and how often, 15% of my readers are using $g(FeedDemon) and 13% use $g(bloglines) (my favor RSS reader)
- How many times an item is clicked
- How many clicks have occurred within the last hour
The list goes on and on. In addition, FeedBurner provides ways to "Optimize" your feed with a whole slew of services that make your feed more useful and user friendly. For example, if you look at the bottom of this entry you'll likely see links for "Email this", "Add a comment", "Add to del.icio.us" and "Digg this". All of these are what FeedBurner calls $g(FeedFlare) which you can enable once you've $g(burned your feed). They even offer a "Pro" level of statistics for those people seriously addicted to numbers breaking things down even further. So, if you publish an RSS feed you should consider "burning" it with FeedBurner.
UPDATE: I totally forgot to mention, FeedBurner also handles the email subscriptions to my RSS feed.