Use explode to separate categories

Although what you are doing is subject to SQL Injection, you can use implode() to transform an array to a string.

Assuming your $ _GET looks like this:

http://site.com.br/filmes?category=acao&category=romance&category=thriller

You could do something like this:

$categoria = $_GET['category'];
$likes = implode("%' OR categoria LIKE '%",$categoria);
/* esse implode faz um array assim:
  [0] => 'acao',
  [1] => 'romantico',
  [2] => 'thriller'

  ficar assim:

  "acao%' OR categoria LIKE '%romantico%' OR categoria LIKE '%thriller"
*/

$sql = "SELECT * FROM filme WHERE categoria IS NOT NULL AND ( categoria LIKE '%$likes%' ) ORDER BY nome LIMIT 25";

The explode() takes a string and becomes an array, for example:

$str = "este,e,um,string";
$array = explode(",",$str);
//devovle:
/*
  [0] => "este",
  [1] => "e",
  [2] => "um",
  [3] => "string"
*/

So to use explode() , $ _GET would have to look like this:

http://site.com.br/filmes?category=acao,romance,thriller

And then the only thing that changes is:

$categoria = explode(',', $_GET['category']);

Elaboration

It has been clarified that your problem is that acao also returns animacao due to the same acao .

In this case, you would have to change your SQL. You have a few options:

Here is a SQLFiddle , showing an example of both.

  

I suggest that you edit your question, because as you mentioned in one answer, your problem is another.

My answer to the problem:

Use this function, called clean , to remove the spaces or traits between the characters:

function clean($string) {
   $string = str_replace(' ', '', $string); // Substitui os espaços vazios.
   $string = str_replace('-', '', $string); // Substitui os traços 

   return preg_replace('/[^A-Za-z0-9\-]/', '', $string); // Remove todos os special chars.
}

echo clean('anim a c a o');
echo '<br />';
echo clean('anim-a-c-a-o');

Output:

animacao
animacao

EXAMPLE ONLINE

Assuming the contents of $_GET['category'] is for example:

$_GET['category'] = "ação, comédia, romance";

You could do this:

$categorias = !empty($_GET['category']) ? $_GET['category'] : '';

$categorias = implode("', '", explode(', ', $categorias));

$sql  = "SELECT * 
         FROM filme 
         WHERE 
            categoria IS NOT NULL AND 
            categoria IN ('{$categorias}') 
         ORDER BY nome LIMIT 25";

The% wrapper% is doing the following:

The $categorias = implode("', '", explode(', ', $categorias)); part explodes the contents of the variable that is explode(', ', $categorias) into an array "ação, comédia, romance" . Then the ["ação", "comédia", "romance"] "paste" content that has been "exploded" in a string using as a separator of each part the string implode("', '", explode(', ', $categorias)) so the result is now% with%.

With this result we can use the condition ', ' of SQL to say that the field must have a value similar to some of the elements or that is "ação', 'comédia', 'romance" which means that the value of the field IN must be equal the categoria IN ('ação', 'comédia', 'romance') or categoria or ação .

Or you can still concatenate multiple% s of% s as you were doing:

$categorias = explode(', ', $categorias);

$sql  = "SELECT * 
         FROM filme 
         WHERE 
            categoria IS NOT NULL AND (";

foreach ($categorias as $categoria) {
    $sql .= " categoria LIKE '%{$categoria}%' OR ";
}

$sql = rtrim($sql, ' OR ') . ") ORDER BY nome LIMIT 25";