Create a plug-in hooked in global-start with this code and then place $threadlist where ever you want the list displayed. The list is not formatted, it just puts each link on a new line, so you will have to do some formatting. Also It will add 1 query to every page.
PHP Code:
$threadlist='';
$last_threads = $vbulletin->db->query("SELECT DISTINCT(threadid), title FROM " . TABLE_PREFIX . "thread ORDER BY rand() LIMIT 0,12");
while ($mthreads = $vbulletin->db->fetch_array($last_threads))
{
$threadlist.= "<a href=\"showthread.php?t=$mthreads[threadid]\">".fetch_trimmed_title($mthreads[title])."</a><br />";
}