What about using the SQL function MIN() to your advantage. Something along the lines of...
$minrow = mysql_query("SELECT MIN(ID) as MinimumID FROM success_stories)";
...
<? if ($id > $MinimumID) { ?>
<a href="success_popup.php?id=<?=$id-1?>"><img src="pix/subnav_success_popup_back.gif" width="102" height="15" alt="back" border="0"></a>
...
Of course, with either this method or the one you posted, you'll need to make sure that there are no skipped records (i.e. ID = 5 doesn't exist, but the lowest is ID = 4). You would probably be better off using the SQL sort feature. Maybe something like...
$result = "SELECT ID, date, name, email, feeling, message FROM success_stories WHERE ID='$id' order by ID DESC LIMIT 0,2");
Then stick the results in an array or two variables and check for the existance of the second before making the link.
Hope that helps.