Registration field custom table location

I am trying to create additional fields in my user registration form using default Drupal field system, but it creates another table in database for itself. What I want to do is to find way to add additional columns into users table.
Is there any way I can change each fields settings?

EDIT:
What I have done so far...
Edited user_account_form() and added this code:

$form['account']['invite_key'] = array(
    '#type' => 'textfield',
    '#title' => t('Invitation key'),
    '#maxlength' => INVITATION_MAX_LENGTH,
    '#description' => t('Random text'),
    '#required' => TRUE,
    '#attributes' => array('class' => array('invite_key')),
    '#default_value' => (!$register ? $account->invitation : ''), 

Now the Invitation key field appears on registration form, but after the registration process no information appears at users table on database.
What I'm missing?