<?php if ( is_singular() ) wp_enqueue_script( 'comment-reply' ); ?>

This code checks if the visitor is browsing either a page or a post and adds the JavaScript required for threaded comments if they are.

I prefer a slight variation

<?php
if ( is_singular() && comments_open() && get_option('thread_comments') )
  wp_enqueue_script( 'comment-reply' );
?>

My variation checks if the visitor is browsing either a page or a post, if comments are open for the entry, and finally, if threaded comments are enabled. If all of these conditions are met, the JavaScript required for threaded comments is added.

If you run your wp_enqueue_script calls in functions.php, as I do, this is the code to use:

<?php
function theme_queue_js(){
if ( (!is_admin()) && is_singular() && comments_open() && get_option('thread_comments') )
  wp_enqueue_script( 'comment-reply' );
}
add_action('wp_print_scripts', 'theme_queue_js');
?>

The call is added to the wp_print_scripts action as is_singular and comments_open are unknown during the init action.

Updated Aug 15 ’09: Fixed two typos in the final code sample

Updated Jun 13 ’10: Changed action in final code block from get_header to wp_print_scripts. Either action works but wp_print_scripts has a closer relationship with the task being performed than the former.

Updated Jul 29 ’10: Removed == 1 from option check, it’s not needed; merged two if statements in final code block into one.

Props to Digging Into WordPress for the …the right way… terminology:)