Google Reader announced in March that they would be shutting down the RSS service, effectively opening the whole internet and RSS back up. The big shutdown is Monday, so I'd make it a goal to move your data out of there this weekend.
Here's what I did:
1) Downloaded my data from Google Takeout. This handy service (although a bit clunky) will let you download your data in an OPML file compressed as a Zip. If all else fails, it's good to have a backup of your data as most services will offer OPML import.
2) Synced with Feedly. Feedly was nearly the first to jump on the Reader shutdown and they have supported importing and syncing your Reader feeds from the get-go. I did this weeks ago, but went back to check that my feeds are fine. You can continue to use Feedly as a Google Reader replacement even after the shutdown. They have apps for all major platforms. Feedly is free.
3) Synced with Digg. Yes, you read that correctly, Digg. Like Feedly, Digg has smartly built an entire backend for importing your feeds to their Reader service. App updates in the last 24 hours will let you even do it from your phone. Digg is also free.
There are many other paid services such as Feedbin, Feed Wrangler, and Fever that I'd love to check out, but for now I just want to make sure my data is intact after 6+ years or reading articles on Google Reader. Additionally, you can listen to the Mac Power Users podcast episode 143 that's all about the big shutdown.
If you download your data and import it to a few services that will work once Google Reader is shut down, I'd say you're in pretty good shape come Monday.