One way to do that is to add some small gadgets that display search results for queries related to your site. You can now add a book bar, a news bar, a video bar or a map. A news bar shows the latest news about your favorite topics, and occupies a very small amount of space, with always up-to-date and hopefully displays relevant news. The downsides are that the widget increases loading time and the animations might become annoying.
It would be interesting if Google combined these solutions with Related Links, that shows news, videos relevant for a page.