untested-
<?php
$text = '
<td><a href="/Business/"><img src="/images/business.gif" width="78" height="17" alt="Business" border="0"></a></td>
<td width="3"></td>
<td><a href="/Desktop/"><img src="/images/desktop.gif" width="69" height="17" alt="Desktop" border="0"></a></td>
<td width="3"></td>
<td><a href="/Development/"><img src="/images/development.gif" width="102" height="17" alt="Development" border="0"></a></td>
<td width="3"></td>
<td><a href="/Education/"><img src="/images/education.gif" width="82" height="17" alt="Education" border="0"></a></td>
<td width="3"></td>
<td><a href="/Games/"><img src="/images/games.gif" width="60" height="17" alt="Games" border="0"></a></td>
<td width="3"></td>
<td><a href="/Internet/"><img src="/images/internet.gif" width="69" height="17" alt="Internet" border="0"></a></td>
<td width="3"></td>
<td><a href="/Multimedia/"><img src="/images/multimedia.gif" width="90" height="17" alt="Multimedia" border="0"></a></td>
<td width="3"></td>
<td><a href="/Utilities/"><img src="/images/utilities.gif" width="67" height="17" alt="Utilities" border="0"></a></td>
';
preg_match_all('/alt="([^"]*)"/i', $text, $matches);
print_r($matches[1]);
?>
to learn more about regex:
http://www.regular-expressions.info/tutorial.html