In case you didn't get the joke, "News for dummies" is just my nickname for the news designed for non-native speakers. It tends to be spoken more slowly and use less advanced vocabulary. I use the term because I'm the dummy, you see. If I were smart, then I'd use the news for native speakers. (Sometimes I give it a shot and then my head explodes. German tends to explode my head more than Swedish.)
In response to my links to the Swedish and German news for dummies, commenter David Conrad asked if there was an equivalent service in French. I don't speak French myself, but a little bit of web searching turned up Le journal en français facile which appears to be the news in easy French. They even have a quiz afterwards to see how good a job you did. And like Deutsche Welle, they also have a series of online French lessons.
Commenter Peter Chen wonders if there's an English news for dummies. A very quick search at the Voice of America News site reveals News in Special English, a service that provides the news and cultural information about the United States in Special English. Analogous with the Swedish Klartext style, Special English uses a reduced vocabulary, avoids idioms, and keeps to a simple sentence structure.
Here one way to find the news for dummies in various languages: Choose a likely country for the language you are interested in. Find the national radio broadcast service for that country. Go to their web site and start poking around. (Of course, you have to be able to read the language you're searching for.) Often—two out of three in today's examples—you will find the "news for dummies" on the front page or close to it.