Drupal - How can I force users to provide a reason when cancelling their accounts?

Here you go, alter the user_cancel_confirm_form.

function MYMODULE_form_user_cancel_confirm_form_alter(&$form, &$form_state, $form_id) {
  $form['reason'] = array(
    '#title' => t('Reason'),
    '#type' => 'textarea',
    '#description' => t('We are sad to see you go, why do you want to leave?'),
    '#required' => TRUE, // force to input
  );

  $form['#submit'][] = 'user_cancel_log_reason'; // add custom submit handler
}

function user_cancel_log_reason($form, &$form_state) {
  $reason = $form_state['values']['reason'];
  // do whatever with the reason, e.g watchdog
  watchdog('user', 'User cancel reason:' . $reason);
}