Tiny Tiny RSS is an open source web-based news feed (RSS/Atom) reader and aggregator, designed to allow you to read news from any location, while feeling as close to a real desktop application as possible.
Tiny Tiny RSS
If you have to right requirements on your server, you can set up your own rss feed reader. If your server is running LAMP, then more than likely you will be able to use this open source.
Server Requirements:
- PHP version 5.3 or newer (detailed PHP requirements)
- PostgreSQL or MySQL (InnoDB is required, MyISAM will not work).