How can you make it so the comment box shows on some pages or posts but not all?

In principle you should be able to achieve that by using categories for your posts. So while your normal loop for the single.php might look like this (I’ll just leave the markup I had in there since I took this out of a file I had lying around. It may of course be different from yours.)

<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
    <?php the_title(); ?>
    <p><em><?php the_date(); ?>, <?php the_time(); ?></em></p>

    <?php the_content(); ?>
  <small>Permalink: <?php the_permalink(); ?></small>

    <hr>
    <?php comments_template(); ?>

<?php endwhile; else: ?>
    <p><?php _e('Sorry, diese Seite existiert nicht.'); ?></p>
<?php endif; ?>

You would get another another if to check if it’s in the category. It should more or less like this Codex article.
So you’ll just have to put the posts in question in a “no comments” category and make sure that this category is displayed without the

<?php comments_template(); ?>

part of the loop. I think you should be fine then.

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