Source code for blog article http://sanchiz.net/blog/block-with-form-configuration

example_block.module

<?php
/**
 * @file
 * Example block
 */

/**
 * Implements hook_block_info().
 */
function example_block_block_info() {
  $blocks['random_numbers'] = array(
    'info' => t('Random numbers'),
  );

  return $blocks;
}

/**
 * Implements hook_block_view().
 */
function example_block_block_view($delta) {
  $block = array();

  switch ($delta) {
    case 'random_numbers':
      $block['subject'] = t('Random numbers');
      $block['content'] = example_block_random_numbers();
      break;
  }

  return $block;
}

/**
 * Implements hook_block_configure().
 */
function example_block_block_configure($delta = '') {
  $form = array();

  switch ($delta) {
    case 'random_numbers':
      $form['random_numbers_count'] = array(
        '#type' => 'textfield',
        '#title' => t('Count numbers'),
        '#default_value' => variable_get('random_numbers_count', 5),
        '#element_validate' => array('element_validate_number'),
        '#required' => TRUE,
      );
      break;
  }

  return $form;
}

/**
 * Implements hook_block_save().
 */
function example_block_block_save($delta = '', $edit = array()) {
  switch ($delta) {
    case 'random_numbers':
      variable_set('random_numbers_count', $edit['random_numbers_count']);
      break;
  }
}

/**
 * Generate random numbers.
 */
function example_block_random_numbers() {
  $numbers = array();
  $count = variable_get('random_numbers_count', 5);
  for ($i = 0; $i < $count; $i++) {
    $numbers[] = rand(0, 1000);
  }
  return theme('item_list', array('items' => $numbers));
}