Google have announced that they're shutting down Google Reader come July 1st:
We launched Google Reader in 2005 in an effort to make it easy for people to discover and keep tabs on their favorite websites. While the product has a loyal following, over the years usage has declined. So, on July 1, 2013, we will retire Google Reader. Users and developers interested in RSS alternatives can export their data, including their subscriptions, with Google Takeout over the course of the next four months
They call it usage decline but it's more likely that most users are simply using it as a sync engine to access their feeds through apps like Reeder. Whatever the reasons, this leaves many of us at a dead end in terms of reading RSS. You can of course export your data and Dave Caolo has outlined the process on 52Tiger. Other have mentioned using services like Flipboard or Pulse but I've always found these apps to be a little bloated and they don't really fit with how I like to consume news. The only viable alternative as of right now is Fever. Fever is a self-hosted aggregator and is supported on iOS by the aforementioned Reeder as well as Sunstroke. Of course, being self-hosted means you're going to have to have somewhere to install it and at least some knowledge of server-side tech. MacStories have got a great tutorial to get you started. There is hope, however, in the form of Feed Wrangler a project by David Smith:
This project is already well along in development, with a working web interface and native apps. I was expecting to launch early this summer but Google has announced that they are closing down Reader July 1. That accelerates my plans and I am now working to get ready for public consumption as soon as possible.
Between Fever, Feed Wrangler as well as projects that haven't been announced yet June might not be so bad for RSS after all.