Search for duplicate or similar node titles when creating content?

I'm not sure if there's a contributed module already. However you can create it yourself.

First you need to create/register autocomplete callback menu using hook_menu function.

/**
 * Implement hook_menu().
 */
function mymodule_menu() {

  $items['mymodule-autocomplete-title'] = array(
    'page callback' => 'mymodule_autocomplete_title',
    'access arguments' => array('view published content'),
    'type' => MENU_CALLBACK,
  );

  return $items;
}

Then create a function to search and retrieve similar node titles.

function mymodule_autocomplete_title($title) {
  $results = array();
  $query = db_select('node', 'n')
    ->condition('n.title', '%' . db_like($title) . '%', 'LIKE')
    ->fields('n', array('title'));

  $nodes = $query->execute();

  foreach ($nodes as $row) {
    $results[$row->title] = check_plain($row->title);
  }

  drupal_json_output($results);
}

Then alter the desired node add form using hook_form_alter function to change normal node title field to autocomplete node title field.

/**
 * Implement hook_form_alter().
 */
function mymodule_form_alter(&$form, &$form_state, $form_id) {

  // node add form id
  if($form_id == 'page_node_form') {
    // make title field autocomplete field  
    $form['title']['#autocomplete_path'] = 'mymodule-autocomplete-title';
  }  
}