Drupal Mysql SSL Connections
The Drupal 7 database layer uses PDO which prior to PHP 5.3.7 did not support MySQL with SSL.

Assuming you're using PHP 5.3.7 or later there is a patch available for Drupal to allow "arbitrary PDO options" to be used, which would include the ability to specify an SSL option.

See this discussion for a fair bit more information and links to the issues on php.net.

EDIT

For Drupal 6 you can change the mysql_connect() line in includes/database.mysql.inc to:

$connection = @mysql_connect($url['host'], $url['user'], $url['pass'], TRUE, MYSQL_CLIENT_SSL);


Although you should really turn this into a patch and apply it to the includes/database.mysql.inc file as hacking core is never a good idea.