1) Choose a URI or ID. Feed ID  
OR
Feed URI  
2) Then choose a number of days. Days  
3) Then choose a type. Type Feed Item
4) Then choose a format. Format RSS HTML  
5) Then click Go.  
FeedBurner offers an API called Awareness which allows you to retrieve the stats they provide by XML-RPC. It's an interesting service, despite the fact that my interest in RSS is entirely academic. FeedBurner politely points its users to Paul Kedrosky's post in which he announces a script that uses AwaPI. It works, of course, but he begs of his users:
Do me a favor and don't beat the tar out of this. Every three hours is plenty frequent to update your feed, and once-daily would be better. People who can't stop themselves from checking their feed stats every thirty seconds are not going to be using my little service for long.
Personally, I find those limitations unacceptable, so I sat down and coded up a free service for myself. While I can't afford to offer my bandwidth to the world, use the service at your own risk. Worse comes to worse, I'll use up my bandwidth for the month and your feeds will stop working. Don't fret, you can always just take the code, in whole or in part.

Please note, connections are only accepted from FeedBurner or this static HTML. If you'd like to use this service in an RSS reader, you must use FeedBurner. Alternatively, if there's an RSS service provider you'd like me to add to the whitelist, please let me know.

If you click on any form element and a "Pro" icon is displayed, that means you need to be a member of Total Stats Pro, a paid service through FeedBurner, to get anything but an error page.