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.
Google tried to repeat the success of the Maps API. "We felt that the Maps API was successful because it was very easy to use, and very easy to explain, where you could show somebody a piece of HTML with some JavaScript, and most anybody could get a map on a webpage very quickly, and have some good eye candy, and some good utility by adding that to their page. What I was interested in is that Google is known for search, and we have search across a wide variety of backends. Could we make search as easy to integrate, and as useful, as we have done with Maps?" explains Mark Lucovsky from Google.
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.