There used to be quite a few problems, when installing Drupal on GoDaddy's shared hosting. There is a lengthy discussion of the related issues. However, recently GoDaddy fixed a few most serious ones, in particular, they gave users permission to invoke MySQL "TABLE LOCK" command, which was the greatest problem of all. So if you deploy Drupal on GoDaddy now, it should be a very straightforward process.
If you want your Drupal to use PHP5 and not PHP4, which is a good idea if you want slightly higher performance and better handling of Unicode, you will need to make adjustments to your .htaccess, since by default files with .php extension are handled by PHP4. Simply add
# use php5 by default<br />
AddHandler x-httpd-php5 .php<br />
AddHandler x-httpd-php .php4
at the top of the file and it should do the trick.
The only remaining problem for Drupal deployment on GoDaddy remains the fact, that they won't let you create temporary tables in MySQL. This doesn't allow you to use Drupal's built-in search. You have to use either Google or upgrade to a virtual dedicated package (considerably more expensive).
Another problem I've noticed recently is the so called "white screen of death" - occasional blank page, returned by Drupal. The annoying thing is that it only happens in Internet Explorer - in Firefox everything works fine. I couldn't investigate the problem in full, since GoDaddy won't give you access to Apache logs, but I could fix the problem by switching the caching off completely.