RSS feeds require a dedicated "reader" to subscribe and read them. There are many applications and apps out there and this will be device- or browser-specific. Here are some several links to both web-based and browser-based (add-ons) feed readers.
Choose your application from the list below for lists of popular RSS-compatible software. For these readers, you will need to copy the above URL and add it into your RSS reader of choice.
InoReader (opens in a new window) is popular RSS reader. It is clean, simple and powerful, and displays articles is several formats. Like many modern web-apps, InoReader offers a full suite of social "sharing" options. It also integrates with many other web-apps, e.g., Pocket, Evernote, and Readability. InoReader provides Android and iOS apps, plus a mobile site (opens in a new window) for other small format devices. There are also InoReader extensions for major browsers.
G2Reader (opens in a new window) is also similar to InoReader. According to their web site, the free version of G2Reader can accommodate up to 100 feeds.
Blogtrotter (opens in a new window) is a unique service that accesses web feeds you subscribe to and relays them to your email inbox. It converts the content to a compact, easy-to-read format. Blogtrotter accepts OPML subscription lists (opens in a new window) so you could use it to replace Google Reader if you only have several feeds you want to follow.
Netvibes (opens in a new window) offers a wide range of "widgets" and apps to access web feeds, tweets and other kinds of dynamic content. For example, there's an app that delivers all the latest news from Google, split up into 8 tabs for World, U.S., Business, Sci/Tech, Sports, Entertainment, Health and Most Popular.
Feedbooster (opens in a new window) has an impressive array of filters -- date, folder, author, source, etc. It's a different way to access articles. Some users will find it works well for them.
AOL (opens in a new window) has a simple but complete web reader. In particular, it makes it easy to open items you're interested in a new tab. After you've got the ones you want load, you can shift to reading them, extracting what you want, etc.
Add-ons/Extensions for browsers and web-apps for smartphones and tablets combine many of the advantages of desktop readers and web-based readers like Google Reader. They have a small footprint and can be "instantly" installed/uninstalled as well. Like web-based readers, an add-on reader creates an efficient browser-centric workspace, with good workflow for feed-based tasks.
Opera has a built-in RSS reader integrated with Opera Mail.
Mozilla maintains a "collection" of popular feed-reader add-ons for Firefox (opens in a new window). You can add them to Firefox directly from the collection page. Brief (opens in a new window) is a Firefox extension and is powerful and simple at the same time. Brief is an excellent, capable replacement for Google Reader. NewsFox (opens in a new window) is another capable add-on that puts a three pane reader (classic email layout) directly in a tab. Both of these Firefox extensions integrate directly with Live Bookmarks. There are also many other feed reader extensions for Firefox (opens in a new window).
NewsBlur (opens in a new window) is an RSS reader that you can "train" (like/dislike) to show you just the kind of posts you want to see from each feed. The free version of NewsBlur is limited to 64 feeds, but that is enough for many users. Free iPad/iPhone apps, Android apps, Windows Phone 8 apps, browser add-ons, and more are offered.
RSS Subscription Extension (opens in a new window) adds RSS feed discovery and subscription options to Chrome. The extension comes with 4 feed readers predefined (Google Reader, iGoogle, Bloglines and My Yahoo). Other Chrome RSS reader extensions can be found in their extensions marketplace.