I came across BookBox this weekend. Although they seem to have been around for a while, it was the first time that I saw one of their videos. Based in India, they make short videos of children’s stories in various languages, including German. Each story has subtitles, so you can read along with it, or you can download the stories as PDFs from the website (make sure it’s set to ‘German’). Even better is their Android app (iPhone not available yet in German). EDIT 2019: The stories can still be downloaded but they now cost $0.99 per story.
I’ve just had great fun watching some of their stories on my phone, but why not watch some yourself?
And if you have difficulties with understanding the German text, watch the videos in English first. If you prefer, you can also buy the stories as kindle books.
Here is the link to their YouTube channel, which shows all videos in the languages available: https://www.youtube.com/user/bookboxinc/featured
Have a look around!