I thought it would be cool too, so I made a quick ‘n dirty plugin to do that very thing:

<?php
/*
Plugin Name: Site Colors
Plugin URI: http://www.alexhemptonsmith.com
Description: Lets you define the header color for specific sites
Author: Alex Hempton-Smith
Version: 0.1
Author URI: http://www.alexhemptonsmith.com
*/

function site_colors(){

 $site = get_current_site();

 // Site with ID of 1 has a header with a red background
 if ($site->blog_id == 1)
 $header_color = 'red';

 // Site with ID of 2 has a header with a black background
 if ($site->blog_id == 2)
 $header_color = '#000';

 if ($header_color)
 echo "<style type='text/css'>#wphead {background: $header_color !important;}</style>";
}
add_action('admin_print_styles', 'site_colors');

You can download the plugin here.