What do you mean 'wrong' with it? What is happening? What isn't happening? How do you know something's going 'wrong' ?
Also, make sure we are notified about every conceivable error by debugging your script:
<?PHP
include("connect.php") or die('Inclusion failed');
//database data is
// userid: asa_carter
// verify: verified
$u = "asa_carternot";
$v = "verifiednot";
$query = "UPDATE login SET verify='verified' WHERE userid='$u' AND verify='$v'";
echo '<hr>(DEBUG) Query is: ' . $query . '<hr>';
$verify = mysql_query($query) OR die('<hr>ERROR! MySQL said: <b>'. mysql_error() . '</b><hr>');
echo '<br>(DEBUG) There were <b>' . mysql_effected_rows() . '</b> rows affected by the UPDATE query.'
?>
Also, what is in connect.php ? Do you assign the MySQL link identifier (returned from mysql_connect() ) to a variable? If so, I would add that as a second arguement to the mysql_query() and as an arguement to the mysql_error() and mysql_affected_rows() as a good coding practice.
Another thing you'll notice I changed in your script was the short-open tag. As a good programmer, this tag is deprecated for compatibility reasons. The short-open tag ('<?' versus the full open tag '<?PHP') is an option, and can therefore be disabled or enabled. Since '<?PHP' isn't an option (as far as I know), you'll never have to worry about using it versus a short-tag.