I have a list of places you would use OOP-Style Classes in my answer to this question:
https://stackoverflow.com/questions/2035449/why-is-oop-hard-for-me/2035482#2035482
Basically, whenever you want to represent an object that has things in it. Like a database variable that has a connection in it that is unique. So I would store that so I can make sure that the mysql_query uses the correct connection everytime:
class MySQL extends Database
{
    public function connect($host, $user, $pass, $database)
    {        
        $this->connection = mysql_connect($host, $user, $pass);
        $this->select_db($database);
    }
    public function query($query)
    {
        return mysql_query($query, $this->connection);
    }
    public function select_db($database)
    {
        mysql_select_db($database);
    }    
}
Or maybe you want to build a Form, you could make a form object that contains a list of inputs and such that you want to be inside the form when you decide to display it:
class Form
{
    protected $inputs = array();
    public function makeInput($type, $name)
    {
         echo '<input type="'.$type.'" name="'.$name.'">';
    }
    public function addInput($type, $name)
    {
         $this->inputs[] = array("type" => $type,
                "name" => $name);
    }
    public function run()
   {
       foreach($this->inputs as $array)
       { 
          $this->makeInput($array['type'], $array['name'];
       }
    }
}
$form = new form();
$this->addInput("text", "username");
$this->addInput("text", "password");
Or as someone else suggested, a person:
class Person{
    public $name;
    public $job_title;
    // ... etc....
}
All are reasons to create classes as they represent something that has properties like a name or a job title, and may have methods, such as displaying a form.