Judging by the amount of activity at http://drupal.org/node/144643 this is common issue for Drupalers.

There are a lot of good reasons to run Drupal in a directory other than root and it has certainly saved me a lot of headaches when clients have asked for something else installed alongside Drupal on the same host and makes staged upgrades a snap.

The process is remarkably simple with a little .htaccess magic.

Assuming you installed Drupal in a sub-directory of your webroot called drupal your root directory .htaccess should look like this:

If you are coming from Joomla! you have not doubt run into some frustrations trying to get Drupal's menus setup the way you want.  The taxonomy_menu module provides an easy way to setup a very similar system in Drupal.  Like most things in Drupal there is a lot more than one way to solve this problem but this is the one that works best for me.