How can I download my Reader data? - Reader Help:

Google Reader will be retired on July 1, 2013. If you'd like to download a copy of all your Reader data before then, you can do so through Google Takeout. You'll receive your subscription data in an XML file, and the following information will be downloaded as JSON files:

Wait, what?  That's evil.  Really, how much overhead can this possibly be?  No explanation given.  Sad.