iGoogle gadgets can now communicate with each other using Google's PubSub framework, which stands for publish-subscribe.
One gadget can essentially be set up to "publish" content to another gadget, which is the "subscriber," meaning information is being sent from one gadget to the other. This currently only works for gadgets on the same page. I'm not sure how this could be used outside of search query results: for instance, viewing a Google news feed could display a word you'd like to find out more about, so perhaps this word could be searched for, with results showing in another gadget, perhaps for images, video, or maps.
Otherwise, as some have suggested, having Google Apps gadgets speak to each other could perhaps lead to easy scheduling options if a Gmail gadget could send information to the Calendar gadget, or a feed or Picasa image could be sent to the Gmail widget. As this new option has been reported as still being very buggy, there's still a lot of details to be fleshed out. No doubt some interesting things will come of it. See more on Google Gadgets here.