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 ('test@test.com', 'test2@test.com')"

$emails = "'email@email.com', 'email2@email.com'";
// example table data for 2 fields in question
Row | Email              |   AddlEmail
1   | email@email.com    |   email3@email.com
2   | email4@email.com   |   email2@email.com
3   | email5@email.com   |   null
4   | email6@email.com   |   email7@email.com

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@email.com', 'email2@email.com'),
  ('email2@email.com', 'email3@email.com'),
  ('email4@email.com', 'email5@email.com'),
  ('email6@email.com', 'email@email.com'),
  (NULL, 'email@email.com'),
  ('email2@email.com', NULL);

SELECT *
  FROM `doubleSelect`
  WHERE Email NOT
  IN (
    'email@email.com'
  )
  AND AddlEmail NOT
  IN (
    'email@email.com'
  )

AND e.Email NOT IN ('test@test.com', 'test2@test.com')
AND e.AddlEmail NOT IN ('test@test.com', 'test2@test.com')

SELECT *
FROM `doubleSelect`
WHERE (Email IS NULL or Email NOT IN ('email@email.com'))
      AND (AddlEmail IS NULL or AddlEmail NOT IN ('email@email.com'))