I got it: Javascript to the rescue.
<form id="form1" name="form1" method="post" action="product.php?ID=<?php echo $row_prods['ID']; ?>">
</p>
<select name="product" id="product" width="160" style="width: 160px"
OnChange="location.href=form1.product.options[selectedIndex].value">
<option value="" selected>Search by Product</option>
<?php
do {
?>
<option value="product.php?ID=<?php echo $row_prods['ID']?>" ><?php echo $row_prods['Name']?></option>
<?php
} while ($row_prods = mysql_fetch_assoc($prods));
$rows = mysql_num_rows($prods);
if($rows > 0) {
mysql_data_seek($prods, 0);
$row_prods = mysql_fetch_assoc($prods);
}
?>
</select>
</form>