Version 1.1 of a front-end editor plugin called The Wunderbar was just released today, and it lets you create editable Widgets just like you’re describing. The Wunderbar adds a WYSIWYG editor to WordPress, like WordPress’s “Front End Editor” but with much greater capabilities. It edits pages and posts with extensive word-proccessor-style formatting options.
The just-released version also allows comments to be edited, plus it adds a Wunderbar widget. The widget works just like the built-in text widget, except this one enables full WYSIWYG editing of the widget contents on any page they appear.
You can learn more about the Wunderbar editing plugin (including a live demo) at terra-virtua.com.