Figured it out. This creates a drop-down that displays the menu item for invoking the action, so you would use this instead of AnAction:

public class YouTubeAction extends ComboBoxAction {

    public void actionPerformed(AnActionEvent e) {

        Application application = ApplicationManager.getApplication();

        YouTubeApplicationComponent youTubeComponent = application.getComponent(YouTubeApplicationComponent.class);

        youTubeComponent.searchYouTube();

    }

   @NotNull

    protected DefaultActionGroup createPopupActionGroup(JComponent jComponent) {

        DefaultActionGroup group = new DefaultActionGroup();

        group.add(ActionManager.getInstance().getAction("SearchYouTube"));

        return group; 

    }

}

Another method on ComboBoxAction is this one, which can return any kind of JComponent:

public JComponent createCustomComponent(Presentation presentation) {

       return super.createCustomComponent(presentation);

}

I learnt a lot from this thread:

http://intellij.net/forums/thread.jspa?messageID=5203185&#5203185

Hi Dmitry,

This is what I mean:

http://blogs.sun.com/geertjan/resource/youtube-movies-in-intellij-toolbar.png

Now, is there a way to open an external browser from one of the IntelliJ APIs? That would be great because then the selected movie would be openable and one could watch it right away.