Similar in some ways to Orangoo.com (see our recent review of Orangoo here), Tiny Tiny RSS is a sweet and simple RSS reader. Add keyboard-based navigation of the feeds and this is a very solid project. GPL licensed, too, so that’s pretty great. You can download the source and run it on your own server.
tiny tiny rss
Rationale
For years I’ve been searching for a perfect RSS aggregator. I tried desktop ones (Straw, Blam!, Liferea) – while nice programs they usually lacked something or were overencumbered with features. Also, desktop aggregators can’t solve the problem of keeping read feeds in sync between different machines.
I tried server-side aggregators, several ones. Unfortunately, I didn’t find anything that felt usable, they had all the problems of classical web applications – clunky interface, no realtime updates, just not designed the way I like it, etc.
Well, then the obvious solution was to write an aggregator myself. I also felt the need to exercise in simple XmlHttpRequest web application programming, so TT-RSS was born. While obviously being on early stages on development and pretty much unfinished it offers a lot of functionality of desktop application while staying on server-side with all the benefits it provides.
Description
Server-side RSS feed aggregator written in PHP and heavily based on XmlHttpRequest and related technologies for user interface and operation.
License
GPL.
Requirements
* Magpie RSS feed parser;
* PostgreSQL or MySQL (InnoDB and version 4.1 required);
Notice the distinct lack of using the term Ajax. No Ajax for this guy–he’s hardcore XMLHttpRequest all the way, baby! 
He has written a lot of neat stuff there. Go check it out!
Visit his site: http://bah.spb.su/~fox/tt-rss/
Via eHub
Yet another AJAX RSS Feed Reader which display RSS Feeds in draggable auto-arranging AJAX Feed Windows which self-updates as RSS Feed is updated.