I have been asked quite often about German songs. As I listen mostly to world music and other music I am not so familiar with German songs.
Here are a few links to websites with songs which are specifically designed for learning German. They also include exercises and worksheets.

Have fun!

<a href="http://www.goethe.de/ins/us/saf/prj/sig/mus/mcv/">http://www.goethe.de/ins/us/saf/prj/sig/mus/mcv/</a>;

<a href="http://www.deutschlern.net/index.php?module=curs&link=cindex&show=941">http://www.deutschlern.net/index.php?module=curs&link=cindex&show=941</a>;

<a href="http://deutschteam.wordpress.com/category/deutsch-lernen-mit-musik/">http://deutschteam.wordpress.com/category/deutsch-lernen-mit-musik/</a>;