Google announced that it's feed reader called Google Reader will be discontinued on July 1, 2013. The below article gives some reasons why this may be.
There are other feed readers available or many now rely on facebook, twitter, or flipboard to bring them content that is most relevant and interesting to them.
Feed Reader or News Aggregator software allow you to grab the RSS feeds from various sites and display them for you to read and use.
A variety of RSS Readers are available for different platforms. Some popular feed readers include Amphetadesk (Windows, Linux, Mac) and FeedReader (Windows). There are also a number of web-based feed readers available. My Yahoo and Bloglines are popular web-based feed readers.
Once you have your Feed Reader, it is a matter of finding sites that syndicate content and adding their RSS feed to the list of feeds your Feed Reader checks. Many sites display a small icon with the acronyms RSS, XML, or RDF to let you know a feed is available. Many will display an orange symbol like the one below to let you know a feed is available.