You can see if there are any errors by using mysql_error():
<?
$username="root";
$password="worm";
$database="worm";
mysql_connect(localhost,$username,$password);
@mysql_select_db($database) or die( "Unable to select database");
$name=HTTP_POST_VARS['name'];
$web=HTTP_POST_VARS['web'];
$query = "INSERT INTO links VALUES ('','$name','$web')";
mysql_query($query);
if (mysql_error())
echo mysql_error();
mysql_close();
?>