Another way of excluding one or more categories from the home page is to add a small piece of code in your template (index.php etc).
Look for (should be somewhere between line 1-20):
<div class="post" id="post-<?php the_ID(); ?>">
Insert this directly above:
<?php if ((in_category(1) || in_category(2)) && is_home() ) continue; ?>
The code in this example looks for posts from categories with id 1 and 2. If they exist and the visitor are on the home page (is_home), they are hidden.
If the visitor are viewing another category page than home, the posts will be visible.
Exclude one category only?
If you only want to exclude/hide one single category from the home page, use this code instead:
<?php if (in_category('1') && is_home() ) continue; ?>
Hiding a category won't make it invisible to the system. If you have specified to show 10 posts in a category page and 3 of the posts are hidden (as described above), the total amount of visible posts will be 7. The system will not add three new posts from the archive since it consider it allready shows 10 (as defined in dashboard). More advanced code is needed to accomplish this.
This solution has been tested in WordPress 2.5