In my search to exclude categories in wordpress, there wasn’t a clear code snippet that was easy to adjust. I thought I would add this snippet to help others.
<?php
$category_id = get_cat_ID('carousel');
$category_id_2 = get_cat_ID('Applications');
$category_id_3 = get_cat_ID('Product Brochures');
$category_id_4 = get_cat_ID('Services Brochures');
query_posts('cat=−'.$category_id.',−'.$category_id_2.',−'.$category_id_3.',−'.$category_id_4);
if(have_posts()): while(have_posts()): the_post();
?>
<!−− add your loop code −−>
<?php endwhile; ?>
<?php else : ?>
<h2><?php _e('Not Found'); ?></h2>
<?php endif; ?>