Users are understandably upset. In a post on the Official Google Reader Blog, Google explained:
There are two simple reasons for this: usage of Google Reader has declined, and as a company we’re pouring all of our energy into fewer products. We think that kind of focus will make for a better user experience.
Boooo. The good news is that you and export your data so that it can be transferred to another service. (For additional options that won't be covered here, see the links below.)
To do that...
Log in to Google Reader.
Go to your Settings.
Under "Import your subscriptions" you'll see "Export your information." Click "Download your data through takeout."
Google will estimate the size of your data. When you see 100% under the squares, click CREATE ARCHIVE.
It may take some time. When it's complete, click DOWNLOAD. The file will save to your computer (or external hard drive).
After the file is saved to your computer, you'll need it to upload to your next RSS service, so remember where it is stored!
Technology Lesson: Web Aggregators
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Technology Lesson: RSS
Powering Down Google Reader, Official Google Reader Blog
A second spring of cleaning, Official Google blog