AideRSS, an RSS feed filtering service, has recently made available a public API. The AideRSS tagline is 'Read what matters' and their mission is to "research every story and filter out the noise, allowing you to focus on what matters most." Josh Catone from ReadWriteWeb last year described the rationale for the service.
AideRSS uses a proprietary algorithm and scoring system based on comments, trackbacks, and usage in other popular sharing services, to identify the best posts for a particular RSS feed, or set of RSS feeds. You can enter a single feed, site (or an OPML file in their API example app Nizz) to identify the area of interest, and in a few seconds get a result (here's a list of posts ranked for ReadWriteWeb).
As you can see in our AideRSS API profile, their API calls mimic the functionality of the service - you can programmatically retrieve a list of posts by the AideRSS categories of good, great, and best (there are no bad posts - only bad RSS readers) or explicitly by PostRank(tm) score. An alternative way to filter posts is to request all the top posts for a particular time period and number of posts desired. For publishers there is an API ping call to inform AideRSS of new posts. An unused OAuth call in the API would seem to indicate AideRSS has future plans for the API that would require authorized access.
The documentation includes a PHP class and a Ruby gem to get you started, and results can be returned in XML, JSON, plain text, or JSONP (JSONP involves cross domain callbacks and is deconstructed with a PHP example here). The licensing agreement for the AideRSS API specifies only non-commercial use.
We're sure there will be more, as the proliferation of communication services adds to the information overload of a hyperconnected world.