Widgets or gadgets or however named are little programs that can be embedded in your website or your netvibes, iGoogle, pageflakes, Facebook etc. . They take the intelligence from other sites on the web and give it to your site. Popular examples are calendars, weather forecasts, tag clouds …. or soon trendalyzer ;). A complex widget is for instance yahoo.pipes. There are thousands of them out there on www.widgetbox.com or www.programmableweb.com.
Official statistics are using RSS feeds extensively, but not the more elaborate widgets (true?). Search widgets could be a first and very useful test case on huge statistics sites where informations are often hidden to impatiently searching users. A small test can be seen on Statistics Switzerland (German , French ). It uses a widget for Google and a widget, that introduces a search tool with user feedback (www.eurekster.com).