Free Open Source, Advance & Web-Based Feed Reader application: rsslounge
rsslounge is an open source, full-featured & web-based RSS feed reader application that is built with PHP-MySQL.
It allows you to read your feeds, categorize or filter them, set priorities & more from an Ajax-based slick interface.
Besides the standard feed items, rsslounge supports images & photoblogs.
For periodically fetching content from feeds, it offers 2 options: cron job or Ajax-based requests (that work while the application is running).
The application makes switching feed readers so easy with the OPML export/import functionality.
Also, rsslounge is a guide-like application for jQuery fans as it makes use of this library fully with the Ajax requests, accordions, sliders, modal boxes & more..
P.S. It works perfectly in all major browsers except IE.