Google News added a new feature that lets you star news stories. If you click on a star next to a Google News cluster, you'll add it to the Starred section and Google will notify you when it finds related articles.
"When you star a story in Google News, it's one way to let us know that you're interested in that subject. When there are significant updates, we will alert you by putting the headline in bold so you can get more information," mentions Google News blog.
For some reason, Google doesn't add the starred news stories to Google Bookmarks and there's no option to star a news cluster after you open it. Another issue is that the Starred section only includes the most recent 20 starred stories.
I don't know if this is best way to use this feature, but you could star news stories to read them later. If you don't already use Instapaper or Read It Later, starring Google News clusters is a great way to save them for later.