This is easy. All you have to do is edit the archives template so that only the post title (aka the permalink) and the post meta data (the date posted) are visible. If you want, you can also use php_the excerpt to post the first few lines of the post or a summary. Try something like this:
<?php while (have_posts()) : the_post(); ?>
<div class="post">
<h2 id="post-<?php the_ID(); ?>"><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a></h2>
<small><?php the_time('l, F jS, Y') ?></small></div>
<div class="entry">
<?php the_excerpt() ?>
</div>
<?php endwhile; ?>
If you want to exclude this option only for certain categories, then you need to look into the Codex documentation of using The Loop, which basically allows you to make arguments based on what the reader is clicking on. For example, in the above code, at the very top you’ll see the line <?php while (have_posts()) : the_post(); ?>. This starts the loop, and basically says, "If there are posts in this selection, then show this information." The Loop ends with: <?php endwhile; ?>
You can set these “Ifs” to look for anything. Take a look around the forums to find out how to set them for certain categories – there is lots of documentation.