playList.setOnMouseClicked(new EventHandler<MouseEvent>() {

    @Override
    public void handle(MouseEvent click) {

        if (click.getClickCount() == 2) {
           //Use ListView's getSelected Item
           currentItemSelected = playList.getSelectionModel()
                                                    .getSelectedItem();
           //use this to do whatever you want to. Open Link etc.
        }
    }
});