Yes you can easily enable subtitles in all WordPress widgets like default WP widgets, widgets your theme provides you and widgets provided by plugins, hacks etc. Widget Subtitle is the new WordPress plugin that provides you easiest way of adding widget subtitles.
Simply install and activate the plugin. Upon activation the plugin automatically adds a new subtitle field in all widgets. Visit Dashboard -> Appearance -> Widgets page and use subtitle text field and add subtitles to your widgets.
All your website widgets keeps working in old way, the plugin doesn’t adds any subtitle to any widget by itself upon activation.