As you may know, the Google Reader reached EOL at the beginning of July and the alternative RSS reader that benefited the most from this situation was The Old Reader, which is a loyal to the features and the design of Google’s Reader.
But because of the high number of users that have migrated to The Old Reader, the developers are not capable of maintaining it anymore, and so, they have decided to make it private. The developers don’t want to monetize this service, and so, they prefer to serve less users well than many users poorly.
Only the users that have signed up before the 13th of March 2013 (meaning that the refugees from Google Reader will be rejected), the ones that have donated in order to support the project will be accepted to the new, private Old Reader.
However, there are many RSS reader alternative, both self hosted with desktop clients.
As desktop RSS readers (or self hosted readers with desktop clients), I have tried (and wrote installation instructions for) the following:
Feel free to test all and choose which one fits your needs best.