No plugin necessary. Simply add this to your functions.php file.

<?php
  add_filter( 'pre_site_transient_update_core', create_function( '$a', "return null;" ) );
  add_filter('site_transient_update_plugins', create_function( '$a', "return null;" ) );
?>

I find that unexpected updates of the core or specific plugins can really mess up a site – and if you’re turning this site over to some users that generally believe updating always improves it – this will help.