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By default, you can use wp_get_archives() to display a list of recent articles. Nevertheless, it doesn’t allow you to set which category to include/exclude from the list. Here’s a way to do that:

<ul>
<?php
  // display recent posts excluding those from certain categories.
  query_posts("showposts=10&cat=-4,-5,-6,-7,-8,-9"); // grab 10 posts, negative to exclude cat IDs

  while (have_posts()) :
    the_post();
?>
  <li><a href="<?php the_permalink() ?>"><?php the_title(); ?></a></li>
  <?php endwhile; ?>
</ul>

The key here is to tweak query_post’s parameter to your liking. “showpost” means how many post you want to display, while “include” can be used both to include or exclude a category. Note that here you used a category ID. Normal number means you include that category, while adding a negative (”-”) symbol before the number means that you exclude that category. You use comma (”,”) to separate multiple IDs.

So, my query_post above can be translated to “get a list of ten most recent posts, excluding those that belongs to category ID 4, 5, 6, 7, 8, 9″.