I try to make web parts move independently between columns. I have the drag-drop code with list items and I want to do drag-drop thing with the web parts. Here is an example web site: http://www.ataturkairport.com/tr-TR/Pages/Main.aspx I hope that I'm on the right way. If I'm not, I can have your suggestions.
With some tweaking you can get Drag and Drop in edit mode to work in SP 2010. http://blog.pixelmill.com/1161/drag-drop-web-parts-not-working-in-sharepoint-2010-custom-master-page/ But that does not seem to be exactly what you are looking for.
I have never seen that sort of behavior duplicated in a SharePoint site. If I were going about recreating it, though, I would do it within a single web part that had some sort of "canvas" allowing the drag and drop arrangement of different widgets. This would allow reordering of the widgets when not in edit mode.
I think the web part zone infrastructure is a little bit too complex to manage in the way that you would like to be able to drag and drop between web part zones outside of edit mode.