I've thought of a place where counterpoint is common in traditional music. Dixieland. Here's an example:

http://www.youtube.com/watch?v=syng46t9YDo&feature=PlayList&p=DF0BAC568FE7371E&index=0&playnext=1

Listen to all the different parts, using different timings, in that song.

==========
Schweik, I agree with you about the imporantance of a tune being up to the individual composer.