I know that similar sites have been talked about in the past, but another forum recently brought NHK News Web Easy to my attention (thanks to gaiaslastlaugh on RevTK).
Like 毎日小学生新聞 it has daily news articles written in a simpler language for foreign learners or kids, complete with furigana for the kanji. It also has a handy button that highlights people and company names to make them clearer, plus a pop-up dictionary with simple definitions for some of the harder words.
Best of all it has an audio recording at the top of the page, so you can listen to the article as you read along.
Then right there on the page you also get a link to the original, non-simplified version of the same article on the full NHK site, if you wish to test yourself on something tougher :)
This is for Japanese learners, but they make a short news article every day, and then translate it to English. Earlier this year I tried to read through it each day, but it is pretty tough so I gave up and started reading G+ updates from AKB-members instead ^^
The site you linked looks much better Elenkis, maybe I will try to start reading news daily again :)
Speaking of news… How many actually don’t know anything about news in their own country but know almost everything that is going on in Japan? I no longer have any clue what is going on in Denmark, but I know which teams Japan are playing against in football lol.