Such functionality is not available. However, all messages have a number starting with 1. If you are just reading emails, then you can cache last opened message number, and next time start to retrieve emails starting from this (cached) number. Another solution is to cache all opened messages (read more) but the trick is how to invalidate the cache in this case.
Quick Example:
$mail = new Zend_Mail_Storage_Imap(array('host' => 'localhost',
'user' => 'root',
'password' => '******'));
$cachedId = (apc_exists('email_id') ? apc_fetch('email_id') + 1 : 1);
for ($id = $cachedId ; $id <= $mail->countMessages() ; $id++) {
echo sprintf('%d, %s <br/>', $id, $mail->getMessage($id)->subject);
}
apc_store('email_id', $mail->countMessages());