SELECT WebUsername,
  WebPassword,
  Active,
  Email,
  AddlEmail,
  ShowYear
FROM Exhibitors e
WHERE e.Active = '-1'
AND e.ShowYear = 2013
AND (e.Email, e.AddlEmail) NOT IN ('[email protected]', '[email protected]')"

$emails = "'[email protected]', '[email protected]'";
// example table data for 2 fields in question
Row | Email              |   AddlEmail
1   | [email protected]    |   [email protected]
2   | [email protected]   |   [email protected]
3   | [email protected]   |   null
4   | [email protected]   |   [email protected]

CREATE TABLE `doubleSelect` (
  `Email` varchar(255) DEFAULT NULL,
  `AddlEmail` varchar(255) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;

INSERT INTO `doubleSelect` (`Email`, `AddlEmail`) VALUES
  ('[email protected]', '[email protected]'),
  ('[email protected]', '[email protected]'),
  ('[email protected]', '[email protected]'),
  ('[email protected]', '[email protected]'),
  (NULL, '[email protected]'),
  ('[email protected]', NULL);

SELECT *
  FROM `doubleSelect`
  WHERE Email NOT
  IN (
    '[email protected]'
  )
  AND AddlEmail NOT
  IN (
    '[email protected]'
  )

AND e.Email NOT IN ('[email protected]', '[email protected]')
AND e.AddlEmail NOT IN ('[email protected]', '[email protected]')

SELECT *
FROM `doubleSelect`
WHERE (Email IS NULL or Email NOT IN ('[email protected]'))
      AND (AddlEmail IS NULL or AddlEmail NOT IN ('[email protected]'))