I'd opt against traditional sources like the Grimm brothers unless it is for students that really specialise in German. There are too many words that have to be explained and are of no use for today's conversation. When I read Grimm stories to my daughter (I do, because I think she should know the tradtion) I often have to explain a word. Nobody uses today 'Hirsebrei', gestiefelt', 'spindeldürr' 'Ebenholz' 'Wackerstein' etc. Imagine me saying in a conversation when you ask me where I plan to go next "I'm going o'er the raging main" just because I have read it in a song.

For more modern stories/writers look for Michael Ende (see Mudguard above, though I'd prefer the Jim Knopf stories of him), see Erich Kästner (Das fliegende Klassenzimmer, Emil und die Detektive, Das doppelte Lottchen). For serious material (allowing political discussions after the reading) look for short stories by Kurt Tucholsky, Heinrich Böll, Wolfgang Borchert.

Only if they really know already a lot of German the old tales are to be recommended.

Wolfgang