system_settings_form() is replaced by \Drupal\Core\Form\ConfigFormBase

Note: As of beta 6, https://drupal.org/node/2407153 makes this partially outdated. Particularly, the getEditableConfigNames() method must now be implemented. See https://drupal.org/node/2407153 for more information.

Drupal 7 and below contained a function system_settings_form() which took over a form's submit function and automatically mapped its fields to variables using the variable system. With the change to the new configuration system, this function was no longer appropriate, therefore it has been removed. Forms using system_settings_form() will have to be converted to form classes extending \Drupal\Core\Form\ConfigFormBase which implement Drupal 8's FormInterface. This provides a consistent submit button and theme definition. As part of the conversion a form submit methods will have to be written for each form by hand. Read more about FormInterface here: http://drupal.org/node/1932058

Note: If your settings form used to relay on $form['array_filter'] = ['#type' => 'value', '#value' => TRUE]; use to add array_filter() manually in submit method.

Drupal 7

function system_site_maintenance_mode() {
  $form['maintenance_mode'] = array(
    '#type' => 'checkbox', 
    '#title' => t('Put site into maintenance mode'), 
    '#default_value' => variable_get('maintenance_mode', 0), 
    '#description' => t('When enabled, only users with the "Use the site in maintenance mode" <a href="@permissions-url">permission</a> are able to access your site to perform maintenance; all other visitors see the maintenance mode message configured below. Authorized users can log in directly via the <a href="@user-login">user login</a> page.', array('@permissions-url' => url('admin/people/permissions'), '@user-login' => url('user'))),
  );
  $form['maintenance_mode_message'] = array(
    '#type' => 'textarea', 
    '#title' => t('Maintenance mode message'), 
    '#default_value' => variable_get('maintenance_mode_message', t('@site is currently under maintenance. We should be back shortly. Thank you for your patience.', array('@site' => variable_get('site_name', 'Drupal')))), 
    '#description' => t('Message to show visitors when the site is in maintenance mode.'),
  );

  return system_settings_form($form);
}

Drupal 8

This example is outdated. Better read Working with Configuration Forms.

/**
 * @file
 * Contains \Drupal\system\Form\SiteMaintenanceModeForm.
 */

namespace Drupal\Core\Form;

use Drupal\Core\Form\ConfigFormBase;

/**
 * Defines a form to configure maintenance settings for this site.
 */
class SiteMaintenanceModeForm extends ConfigFormBase {

  /**
   * {@inheritdoc}
   */
  public function getFormID() {
    return 'system_site_maintenance_mode';
  }

  /**
   * {@inheritdoc}
   */
  public function buildForm(array $form, FormStateInterface $form_state) {
    $config = $this->config('system.maintenance');
    $form['maintenance_mode'] = array(
      '#type' => 'checkbox',
      '#title' => t('Put site into maintenance mode'),
      '#default_value' => $this->state->get('system.maintenance_mode'),
      '#description' => t('Visitors will only see the maintenance mode message. Only users with the "Access site in maintenance mode" <a href="@permissions-url">permission</a> will be able to access the site. Authorized users can log in directly via the <a href="@user-login">user login</a> page.', array('@permissions-url' => $this->url('user.admin_permissions'), '@user-login' => $this->url('user.login'))),
    );
    $form['maintenance_mode_message'] = array(
      '#type' => 'textarea',
      '#title' => t('Message to display when in maintenance mode'),
      '#default_value' => $config->get('message'),
    );

    return parent::buildForm($form, $form_state);
  }

  /**
   * {@inheritdoc}
   */
  public function submitForm(array &$form, array &$form_state) {
    $this->config('system.maintenance')
      ->set('enabled', $form_state['values']['maintenance_mode'])
      ->set('message', $form_state['values']['maintenance_mode_message'])
      ->save();

    parent::submitForm($form, $form_state);
  }

}

Note that the system_config_form() helper that was added during Drupal 8 development has been removed.