For everyone who uses Google Reader, you've surely heard that Google is discontinuing it tomorrow. It will be the shout heard round the internet...
Anyway, the most important thing is that you go to this Google Takeout page, log in, then click "Create" archive. After a minute or so you'll be able to download the archive as a .zip file. Supposedly other products will let you import those files.
In the meantime, most people suggest Feedly. I've been using it for a day and it's pretty much the same, with a slightly confusing interface.
Interestingly you authenticate via Google -- basically Feedly asks Google to figure out who you are, then they trust what Google tells them), then it imports all your feeds and read/unread status. More info from Feedly on the whole transition here.
Hope that helps someone.