Sometimes, you may have a reason not to update certain plugins. Maybe the plugin was heavily customized or the newer version asks you to pay to continue using it (in my case this is the reason).
Because of that, you may not want to received notification to update the plugins. You may accidentally update the plugins if the notification was turned off.
To remove update notification. Add the following code in main plugins php file.
add_filter('site_transient_update_plugins', 'remove_update_nag');
function remove_update_nag($value) {
if ( isset( $value ) && is_object( $value ) )
unset( $value->response[plugin_basename(__FILE__)] );
return $value;
}