If you want to monitor the latest news about global warming, Google or your favorite basketball team, there's a newsbar gadget for the Personalized Homepage that shows the headlines at the top of the page and news snippets in the gadget container.
There's also a videobar that shows the top 8 search results from Google Video and YouTube for a list of queries. You could include a list of your favorite artists, TV shows or video series (like Google Techtalks) and the videos are always accessible from your personalized homepage (unless, of course, they are removed by the content providers).
These gadgets, but also Google mini search (that lets you search Google without leaving the page) and Google Map search were implemented using Google AJAX Search API. The API lets you build controls and gadgets centered around search, even if this isn't obvious.
They build different solutions that could be just copy-pasted on a site and also these gadgets for Google Personalized Homepage. And because they use AJAX, you can search and see the search results on the same page that contains the gadgets.