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Fianally Digg launched their API :

The Digg Application Programming Interface (API) has been created to let users and partners interact programmatically with Digg. The API returns Digg data in a form that can be easily integrated into an application or a web site.

See the documentation at http://apidoc.digg.com/

Here's some interesting parts from their docs:

Be Polite, Please!

Use good judgment when designing your application. Don't make repeated requests for the same data frequently. […] We monitor API usage, and we may block applications that do silly things.

They also launched a contest for using this API.

Google has just launched their AJAX Feed API:

With the AJAX Feed API, you can download any public Atom or RSS feed using only JavaScript, so you can easily mash up feeds with your content and other APIs.

It requires JavaScript knowledge to integrate with any website, but it's all documented by Google and not hard to do.