Feed readers (aka RSS readers) let you read the feeds of blogs, news sites, etc. — either just the headlines, or the headlines and a short description (or even the whole text) of each item. Wagn has feeds which can be read in any feed reader:
On Recent Changes, or any Search card, you'll see the feed icon in your web browser address bar — usually something like . Clicking on it will let you subscribe to the feed. If you use a separate feed reader, you can subscribe to the web address of your Recent Changes page — something like http://yourdomain.org/recent.
Most web browsers can subscribe to feeds, and feed reading is built into many news or multi-purpose websites (such as Slashdot or My Yahoo). If you're following a lot of feeds, consider specialized web services and downloadable programs as they offer more features such as better management of your feeds, the ability to read them in one big "river of news" (or in groups of related kinds), built-in blogging tools, etc. A few dedicated feed readers are listed here; feel free to suggest more ways that you read feeds.
The whole point of feeds is that you should be able to access them by whatever means you find most convenient. See this article, Five unlikely but great ways of reading feeds to learn how to get feeds by email, Twitter, etc.
Also see directories for Linux, Mac and Windows.