Haochi from Googlified pointed me to a YouTube video from Bill Kee, product marketing manager at Google. The video showcases a Google Talk gadget for the personalized homepage -- it is very polished, and even has some unique functionality that hopefully makes it into the real client one day.
For example, now you can share YouTube videos and Picasa Web Album pictures by simply pasting a link. You, and the person on the other end (if they are using the same gadget) will see a small version of the video or picture right inside the chat window.
The Gadget isn't currently available, but it should be soon. Keep your eyes on http://talk.google.com -- that is where it is set to be posted.
It is now available -- works great!