Sorry, I did not look carefully at your post and assumed that you had extracted the result set into an array named $row. You have not. Instead, you retrieved the first row from the result set into $row, thus $row is not an array of rows, but an array of fields.
The solution is as devinemke described. Change:
$row = mysql_fetch_row($result);
echo $row[0]
To something like:
while ($row = mysql_fetch_row($result)) {
echo $row[0] . "<br />\n";
}
Though I would prefer devinemke's example of using mysql_fetch_assoc() instead of mysql_fetch_row() as it can improve readability.