There are two simpletest modules for Drupal 6.  The 2.x branch (currently at 6.x-2.5) is a backport of the unit testing framework that will be included in Drupal 7.

Unfortunately, error handling is not very good and it is possible to get inscrutable errors like this when running a test:

Running SimpleTests

An error has occurred.
Please continue to the error page
An error occurred. /batch?id=30&op=do

One possible reason for this error: some methods in the simpletest module depend on the PHP DOM package.  DrupalWebTestCase's parse() function contains this line:

       @$htmlDom = DOMDocument::loadHTML($this->_content);

The PHP installation on Fedora does not necessarily include this package, so it's necessary to install PHP DOM support with:

yum install php-xml
sudo /etc/rc.d/init.d/httpd restart