You want to find and read RSS (Really Simple Syndication) feeds on the Internet.
Using downloadable software
A variety of freeware and shareware will let you find and read RSS feeds:
RSS and a competing format, Atom, allow web sites and blogs to syndicate news and information from their sites and feed them to anyone interested. RSS uses XML to create the feeds, and RSS readers are capable of reading that XML and displaying them as news feeds.
RSS readers include built-in ways to find RSS and Atom feeds using search tools, subscribe to them, and will then automatically grab those feeds and display them for easy reading. They'll also allow you to easily organize your feeds and search through them. You can also use the readers to unsubscribe as well.
When you come across an orange box on a web site with the letters "XML" on it, that means the site has an RSS feed. To subscribe to the feed, right-click it, and then either copy the link location and pop it into your RSS reader, or else choose an option that will automatically subscribe to it in your RSS reader. The exact way you do it varies from RSS reader to RSS reader.
Sites that will let you search through RSS feeds for ones you want include http://www.syndic8.com, http://www.newsisfree.com/sources/bycat, http://www.rssreader.com/rssfeeds.htm, and http://www.feedster.com.