Display random posts, but omit the post it is on?

Check to see if you have a post ID (which you should on a single post page but I am not sure if this is in single.php or some other template like index.php) and add that to the $args if you do.

$args = array( 'numberposts' => 3, 'orderby' => 'rand' );
if (is_singular() && isset($post->ID)) {
  $args['exclude'] = array($post->ID);
}
$rand_posts = get_posts( $args );

Reference

http://codex.wordpress.org/Function_Reference/is_singular
http://codex.wordpress.org/Template_Tags/get_posts
http://codex.wordpress.org/Function_Reference/get_pages

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