A have recently set up a "visible only to users I choose" blog here at WordPress.com. From http://faq.wordpress.com/2006/10/23/feeds-and-password-protected-blogs/ I gather that it is not possible to feed off a password protected blog, as it says so. Fair enough... However, I have successfully done this nonetheless, using Firefox's Live Bookmarks. It works fine for a while and then suddenly stops working. I have not been testing it sufficiently to be able to say anything about specific times that this possibility occurs but it has done so several times. It was pointed out to me by a user of our blog that didn't know about the no-feed for pass protected blogs policy.
While it is certainly wise not to have public feeds for private blogs, I was wondering why it is not possible to get a feed when you're logged in? Is it not just checking for a cookie? That way one could log in, keep the browser open in the background and do other stuff while having an email client checking the feed from time to time... Would be very useful!