Breaking News is a well-known website posting news snippets from all over the world from a great variety of news sources. The website keeps getting updated as the stories break/news sources get updated.
The website lets you search for a specific topic that might be of interest to you and lets you select whether you want to get updates on important news and even news from all sources, which pretty much gives you a huge list of news items to read through.
You can even submit a link with your very own breaking news to be listed on the website. (I am not sure whether the submitted link goes through screening first).
I like following news using the Breaking News website by having it open in separate window (on a second screen), and just letting it update with the latest stories.
The Breaking News website also has an associated application for your mobile device, which brings you all the latest news right on your handheld. The app even offers push notifications of the latest stories which is pretty convenient if you are following a hot news story on the go.