Web based RSS aggregators (open source)
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Mark Irons unnamed Perl aggregator. Lightweight, CSS scriptable. Uses XML::Simple.
Meerkat. Insane. Uses XML::Simple.
Feed on Feeds. PHP. RSS and Atom. Barfs on broken feeds (see todo: "Find a way to handle broken feeds better."). But then, probably all of these do. Uses Magpie.
Blagg. Perl, integrates with Bloxom, with plugins for MT. Uses regexps.
Drupal's web based aggregator. Requires Drupal. ;)
Feed on Feeds looks the most promising. Rasterweb has done some customization to Feed on Feeds and likes its hackability (and he's a Perl programmer, so that's saying something about a PHP app). See: Super-Happy-Terrific Aggregator, Super-Happy-Terrific FEED ON FEEDS? (dicusses using Universal Feed Parser), FEED ON FEEDS ala Bloglines, Feed on Feeds Unread List, More Aggregator Madness, Yet More Aggregator Madness.
I think it would be possible to use the Universal Feed Parser to poke data into Feed on Feeds database.
Update: Ohhh, someone already modified Feed on Feeds to use UFP. Simple Aggregator.
Update 2: I shouldn't have started writing all that crap about hacking Feed on Feeds before reading the links off of Rasterweb. Temboz is a Python RSS aggregator that uses SQLLite, Cheetah tempates, and the UFP.
That sounds very much like what I want (though having a built-in webserver is not). But it's not released yet, and it's unclear it ever will be.