There are 2 ways to exclude certain categories from your blog, one is use wordpress plugin named Advanced Category Excluder. This plugin was born because there was a no other real alternative to enable content sparationd and some CMS like functionalities in WordPress. The main goal was, to enhance WordPress’s functionalities, to hide some unwanted categories, from defined parts of the blog.

The alternative way is without plugin, you can add the below code inside the loop then it will work.

<?php
if ( have_posts() ) : query_posts($query_string .'&cat=-1,-2'); while ( have_posts() ) : the_post();
?>