For most commented posts you can use a custom loop in the sidebar for example:
<h3>Most Commented Posts</h3>
<?php $most_commented = new WP_Query('orderby=comment_count&posts_per_page=5');
if($most_commented->have_posts()) : ?>
<ul class="most-commented-posts">
<?php while($most_commented->have_posts()) : $most_commented->the_post(); ?>
<li><a href="https://wordpress.stackexchange.com/questions/38006/<?php the_permalink() ?>" rel="bookmark" title="<?php the_title_attribute(); ?>"><?php the_title(); ?> (<?php comments_number('0','1','%'); ?>)</a></li>
<?php endwhile; ?>
</ul><!-- most-commented-posts -->
<?php endif; wp_reset_query(); ?>
For the top commenters you can use something like this:
And for comment stats like total comments, etc. use this function:
function comment_stats() {
global $wpdb;
// approved responses (comments and trackbacks)
$comment_stats['total_responses'] = $wpdb->get_var("SELECT COUNT(*) FROM $wpdb->comments WHERE comment_approved = '1'");
// trackback count
$comment_stats['total_trackbacks'] = $wpdb->get_var("SELECT COUNT(*) FROM $wpdb->comments WHERE comment_type="pingback" OR comment_type="trackback"");
// comments count
$comment_stats['total_comments'] = $comment_stats['total_responses'] - $comment_stats['total_trackbacks'];
// Akismet spam captured
if(function_exists('akismet_count')) {
$comment_stats['spam_blocked'] = akismet_count();
}
if(!empty($comment_stats)) {
$html .= "<ul class=\"comments-stats\">\n";
foreach($comment_stats as $stat => $stat_value) :
if(isset($stat_value) && $stat_value > 0) {
$stat_name = str_replace("_", " ", $stat);
$html .= "<li>" .ucwords($stat_name). " : " .number_format($stat_value). "</li>\n";
}
endforeach;
$html .= "</ul>\n";
echo $html;
}
}