The first thing to do is to create the function. Paste the code below into your functions.php file:

/**
 * Build a list of all websites in a network
 */
function wp_list_sites( $  expires = 7200 ) {
   if( !is_multisite() ) return false;

   // Because the get_blog_list() function is currently flagged as deprecated
   // due to the potential for high consumption of resources, we'll use
   // $  wpdb to roll out our own SQL query instead. Because the query can be
   // memory-intensive, we'll store the results using the Transients API
   if ( false === ( $  site_list = get_transient( 'multisite_site_list' ) ) ) {
      global $  wpdb;
      $  site_list = $  wpdb->get_results( $  wpdb->prepare('SELECT * FROM wp_blogs ORDER BY blog_id') );
      // Set the Transient cache to expire every two hours
      set_site_transient( 'multisite_site_list', $  site_list, $  expires );
   }

   $  current_site_url = get_site_url( get_current_blog_id() );

   $  html = '
<ul id="network-menu">' . "\n";

   foreach ( $  site_list as $  site ) {
      switch_to_blog( $  site->blog_id );
      $  class = ( home_url() == $  current_site_url ) ? ' class="current-site-item"' : '';
      $  html .= "\t" . '
<li id="site-' . $  site->blog_id . '" '="" .="" $  class=""><a href="' . home_url() . '">' . get_bloginfo('name') . '</a></li>

' . "\n";
      restore_current_blog();
   }

   $  html .= '</ul>

<!--// end #network-menu -->' . "\n\n";

   return $  html;
}

Once done, you can use the wp_list_sites() function in your theme files. The example below shows how it works:

<?php
// Multisite Network Menu
$  network_menu = wp_list_sites();
if( $  network_menu ):
?>
<div id="network-menu">
   <?php echo $  network_menu; ?>
</div>

<!--// end #network-menu -->
<?php endif; ?>

Thanks to Kevin Leary for the great hack!