Brian Littleton's Web Notebook
This is a lot easier than one might think but there is a lot of misleading (due to older versions of Wordpress being different) information out there - so I decided to post this once I pieced it all together.
1. Find the category that you want to exclude - you need the category number specifically.
2. While many people find editing core functions of Wordpress intimidating - it isn't that bad and sometimes is easier than a plug-in that you will then need to worry about updating, etc...
3. Go to your core Wordpress code on your host and navigate to the wp-includes directory.
4. Open the file: default-widgets.php
5. Search for the phrase "wp_list_categories"
6. The full phrase you should see there will look like "wp_list_categories(apply_filters('widget_categories_args', $cat_args));"
7. Right before that phrase, type the following:
$cat_args['exclude'] = 'PUTTHENUMBERYOUWANTTOEXCLUDEHERE';
8. Careful of all the syntax, don't forget the semi-colon there at the end (see above).
9. You can add any other filters by doing the exact same thing just repeated - they are all listed here: http://codex.wordpress.org/Template_Tags/wp_list_categories
If they didn't want us editing core files, then why not put some of these options in the default widget?