On Saturday I tried upgrading to Drupal 6 (from 5.5) and the upgrade scripts failed resulting in a rather horrible frankensite. I have not had time to debug the issue (it appears to have been a table conflict resulting in many invalid SQL statements that ended up corrupting the database used by Drupal). The good news is that recovery is quick and painless.
If you have not yet upgraded make sure you have a backup of your database, and install into a new location, not over your existing install (you can use symbolic links to preserve the name of the location you install to). To backup your database you can use mysqldump:
mysqldump -u adminuser -p databasename > backupfile.sql
where adminuser is the admin user account of your database server, databasename is the name of your drupal database, and backupfile.sql is the backup file that will be created. It will prompt you for your adminuser password.
To restore after the Drupal upgrade script does horrible things to your site, you need to:
Your site should now be restored and ready to use.