I'm a combination Drupal and WordPress developer and have recently started playing with Drupal's Panels module -- which allows you to create flexible layouts and drop content blocks (The Drupal equivalent of widgets) in place on either a per-layout or per-content item basis.
I'm now working on a WordPress project that would really benefit from this kind of functionality — is there a visual layout editor for WordPress that even slightly resembles Panels?
By "visual layout editor", I mean something that can have text and/or widgets added on an ad-hoc basis to regions created by either dragging column widths or click-and-dragging selections (Similar to Adobe InDesign).
Edit: It's a year later, so I've created a wiki answer below. The original question has been updated to reflect this.