Code to edit the admin bar/toolbar in WordPress

Edit Admin Bar.php

// Remove links from the admin bar/toolbar

function remove_admin_bar_links() {
  global $wp_admin_bar;
  $wp_admin_bar->remove_menu('wp-logo');
  $wp_admin_bar->remove_menu('updates');
  $wp_admin_bar->remove_menu('search');
  $wp_admin_bar->remove_menu('comments');
	
  // Remove site name and new only if user is not administrator
  if ( !current_user_can( 'manage_options' ) ) $wp_admin_bar->remove_menu('site-name');
  if ( !current_user_can( 'manage_options' ) ) $wp_admin_bar->remove_menu('new-content');
	
  // Jetpack links
  $wp_admin_bar->remove_menu('notes');
  $wp_admin_bar->remove_menu('stats');
}

add_action( 'wp_before_admin_bar_render', 'remove_admin_bar_links' );

/*
Here are more options to add into remove_menu():

wp-logo: WordPress logo
my-account: Links to your account. The ID depends upon if you have avatar enabled or not.
site-name: Site name with other dashboard items
my-sites : My Sites menu, if you have more than one site
get-shortlink : Shortlink to a page/post
edit : Post/Page/Category/Tag edit link
new-content : Add New menu
comments : Comments link
updates : Updates link
search: Search box
*/