If you don't want to use a contrib module (one does exist), you can implement hook_entity_info_alter() to add the view mode yourself. For example this code adds a new view mode called "Test View" to the node entity type:

function MYMODULE_entity_info_alter(&$info) {
  $info['node']['view modes']['test_view'] = array(
    'label' => 'Test View',
    'custom settings' => TRUE
  );
}

After a cache clear that view mode will appear in all the places you'd expect (manage display, views, etc.)

As far as implementing a new view mode yourself goes it's pretty easy, without any contrib modules.

You can implement hook_entity_info_alter() to add a custom view mode to any entity. For example this code adds a new view mode called "Test View" to the node entity type:

function MYMODULE_entity_info_alter(&$info) {
  $info['node']['view modes']['test_view'] = array(
    'label' => 'Test View',
    'custom settings' => TRUE
  );
}

After a cache clear that view mode will appear in all the places you'd expect (manage display, views, etc.)