Lots of people use Google Reader as their RSS feed reader, including a few thousand who follow this blog using the RSS feed. Google is shutting down Google Reader as of July 1st. Here's how you can backup your subscriptions and a great replacement you can use.
You can export your Google Reader Data (subscriptions) using Google Takeout. Google Takeout actually lets you export pretty much all your Google account data. You go to Google Takeout, and go to the Reader page and click "Create Archive". This will then download all of your feeds, people you follow, starred items and more. When the file is completed, click download. The subscriptions.xml file in the zip file is your subscriptions that you will need to import into other readers.
The app I am using to replace Google Reader is Feedly. It has a web version, plus an Android and iOS app. It's easy to use, can be setup to look like Google Reader, or even better with some cool views with pictures and preview text. The apps sync with the web so no matter what device you use, your feeds will be up to date. It's also free. I've been using it for about a month and love it.
Feedly even has a one-click Google Reader import to make it easy to switch.
Remember, you need to export your data, or import into Feedly before July 1st!
Google Takeout - Take your Google Account Data with you (or just back it up)
Why I Use Google's Products as an Educator