Wordpress - Loading scripts only if a particular shortcode or widget is present

You can use the function is_active_widget . E.g.:

function check_widget() {
    if( is_active_widget( '', '', 'search' ) ) { // check if search widget is used
        wp_enqueue_script('my-script');
    }
}

add_action( 'init', 'check_widget' );

To load the script in the page where the widget is loaded only, you will have to add the is_active_widget() code, in you widget class. E.g., see the default recent comments widget (wp-includes/default-widgets.php, line 602):

class WP_Widget_Recent_Comments extends WP_Widget {

    function WP_Widget_Recent_Comments() {
        $widget_ops = array('classname' => 'widget_recent_comments', 'description' => __( 'The most recent comments' ) );
        $this->WP_Widget('recent-comments', __('Recent Comments'), $widget_ops);
        $this->alt_option_name = 'widget_recent_comments';

        if ( is_active_widget(false, false, $this->id_base) )
            add_action( 'wp_head', array(&$this, 'recent_comments_style') );

        add_action( 'comment_post', array(&$this, 'flush_widget_cache') );
        add_action( 'transition_comment_status', array(&$this, 'flush_widget_cache') );
    }

Just wanted to share a solution I worked on which allowed me to be a bit more versatile with my implementation. Rather than having the function check for a variety of shortcodes, I modified it to seek out a single shortcode that references a script/style function that needs to be enqueued. This will work for both methods in other classes (such as plugins that may not do this themselves) and in-scope functions. Just drop the below code in functions.php and add the following syntax to any page/post where you want specific CSS & JS.

Page/Post Syntax: [loadCSSandJS function="(class->method/function name)"]

functions.php code:

function page_specific_CSSandJS( $posts ) {
  if ( empty( $posts ) )
    return $posts;

  foreach ($posts as $post) {

    $returnValue = preg_match_all('#\[loadCSSandJS function="([A-z\-\>]+)"\]#i', $post->post_content, $types);

    foreach($types[1] as $type) {
      $items = explode("->",$type);
      if (count($items) == 2) {
        global $$items[0];      
        if( method_exists( $$items[0], $items[1] ))
          add_action( 'wp_enqueue_scripts', array(&$$items[0], $items[1]) );
      }
      else if( !empty( $type ) && function_exists( $type ))
        add_action( 'wp_enqueue_scripts', $type );
    }
  }

  return $posts;
}

This will also allow you to add as many as you want on a page. Keep in mind that you do need a method/function to load.

with Wordpress 4.7 there is another way to achieve this in your functions.php file,

add_action( 'wp_enqueue_scripts', 'register_my_script');
function register_my_script(){
  wp_register_script('my-shortcode-js',$src, $dependency, $version, $inFooter);
}

first you register your script, which doesn't actually get printed on your page unless your enqueue it if your shortcode is called,

add_filter( 'do_shortcode_tag','enqueue_my_script',10,3);
function enqueue_my_script($output, $tag, $attr){
  if('myShortcode' != $tag){ //make sure it is the right shortcode
    return $output;
  }
  if(!isset($attr['id'])){ //you can even check for specific attributes
    return $output;
  }
  wp_enqueue_script('my-shortcode-js'); //enqueue your script for printing
  return $output;
}

the do_shortcode_tag was introduced in WP 4.7 and can be found in the new developers documentation pages.