Having built sites on Godaddy technology and Hostgator I've found that getting all of the kinks worked out for the Drupal Clean URL feature can be quite tricky, for that reason I've summarized the different ways to get it working with Godaddy or my company Sustainable Online Solutions below.
The first challenge I ran into is that I overwrote the php.ini file that Godaddy had originally installed by default with my basic one containing the following info. Why did I do this? Well, I had to do it to get things working on Hostgator so I assumed it would be the same at Godaddy, not so...
Hostgator solution for Drupal Clean URL's, create a php.ini file with the following line. If you use Godaddy do not create this file, it is already on the server configured correctly.