Gregarius is a web-based RSS/RDF/ATOM feed aggregator, designed to run on your web server, allowing you to access your news sources from wherever you want.
Tiny Tiny RSS
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.
Feed On Feeds
Feed On Feeds is a server side, multi-user RSS and Atom aggregator! A news aggregator allows you to subscribe to news sources and have new items collected together on a single page. The newest items appear at the top, and you can mark old news items read.
selfoss is a new multipurpose rss reader, live stream, mashup, aggregation web application. selfoss supports all modern browsers, including Mozilla Firefox, Safari, Google Chrome, Opera and Internet Explorer. You can easily add your own data sources. Spouts (aka plugins) fetch the content from the different sources.
SimplePie is a very fast and easy-to-use class, written in PHP, that puts the “simple” back into “really simple syndication”. Flexible enough to suit beginners and veterans alike, SimplePie is focused on speed, ease of use, compatibility and standards compliance.