Okay, following moshu's suggestion, I created a custom page template 'mostviewed.php' by copying page.php, and here is the relevant piece that uses the 'get_posts()' command suggested above:
<h2><?php the_title(); ?></h2>
<div class="entry">
Here are some of my posts that are visited more often than others.
<?php get_posts(array('include' => '70,44,48,21,24,22,11,65,51,96,97,40,91')); ?>
<?php the_content('<p class="serif">Read the rest of this page »
'); ?>
<?php link_pages('<strong>Pages:</strong> ', '
', 'number'); ?>
</div>
Then I created an empty page with this page template. But I still get this empty page, and not this that I wanted (post IDs in get_posts() correspond exactly to this list). What am I doing wrong? Thanks.