Gmail has a very cool feature not available in other webmail applications: feeds for unread messages. For example, the feed http://mail.google.com/mail/feed/atom/ shows the most recent unread items from your inbox. Gmail also offers feeds for your labels: http://mail.google.com/mail/feed/atom/labelname/, but it would be nice to have a comprehensive listing of all the unread messages, not just the ones that have a certain label. As you probably know, "unread" is one of the many built-in labels in Gmail, so you can use it to obtain this feed: http://mail.google.com/mail/feed/atom/unread/. In the URLs above, you can replace "http" with "https" for more security.
Gmail's feeds require authentication, so they don't work in many feed readers, like Google Reader or iGoogle. There are some feed readers that support password-protected feeds:
* assuming you're logged in to your Gmail account, you can add any of the feeds to Firefox's Live Bookmarks (this is more like a workaround than true support for authenticated feeds)
* you can subscribe to the feeds in Opera if you don't like the built-in mail client
Desktop feed readers
* some desktop feed readers listed by Google that support Atom 0.3, SSL/HTTPS, and HTTP authentication
Online feed readers
* Netvibes is a notable example of online feed reader that supports authenticated feeds
Gmail recommends to make sure that the feed's content is private. "Keep in mind when you subscribe to your Gmail feed that some aggregators allow you to share, syndicate, or otherwise re-publish the feeds you subscribe to. This means that even though your Gmail feed is private, its contents could be made public through one of these methods. So you'll want to double-check the privacy settings in your aggregator to make sure you aren't sharing any information you don't want to."