Maybe you are a teacher in search for materials for your class. Maybe you are a parent in search for listening practice for your kid. In m opinion, children should be exposed to the English language on a regular basis: daily if possible.
Here you will find a list of websites where you will find lots of useful podcasts for children and beginners:
Rong-chang.com Easy short stories for children and ESL/EFL beginners.
Hello-World.com Simple dialogues for non-native speaking children.
eslfast.com. A free site with lots of short stories and conversations.
Real English. with some sample listenings.
Adele's corner. Easy online listening activities with blank filling exercises.
About.com English listening comprehension exercises for basic listening skills.
EnglishLingQ.com Graded podcasts.
Randall's ESL Cyber Listening Lab. See the section "Basic Listening Quizzes" with short listening activities for beginning and intermediate students.
Select-Language.com is an interesting site with graded audio-postcards from different English speaking communities.
Finally, these sites are also quite interesting: