Was spinning my wheels today trying to figure out why the comments were not working correctly on my blog.  I was receiving the following error:

"user warning: Duplicate entry '0' for key 1 query: INSERT INTO comments...."

The fix was found here. Evidently it was broken after upgrading from Drupal 5 to Drupal 6.  Simply needed to run the following SQL command:

alter table comments modify cid int(10) auto_increment;

Hope this helps someone else!