Google provides different ways to access Gmail emails. One way is support for Atom which can be used with an aggregator ( newsreader, feed reader, or RSS/Atom reader) to receive new message alerts mainly preview of messange with a link to gmail.
The RSS Feed URL ‘https://mail.google.com/mail/feed/atom’ officially provided by Google requires a RSS Reader which supports subscribing to authenticated feeds i.e one lets you enter Gmail address and passwords. Google Reader doesn’t support feeds protected by passwords.
FreeMyFeed.com is a free web service that lets you re-package authenticated feeds without the password requirement by acting as a go-between. This causes certain lag between the time feed is published and received. To use, go the site and enter the above Gmail RSS URL, username and password and submit. The new URL that you receive can be added in Google Reader.
Note : FreemyFeed.com states that Usernames, passwords, feed URLs and feeds are never stored on the server and are only parsed from the alternate URL to retrieve your feed on the fly from the original source and then are discarded.