Tab dragging (drag and drop to move the tabs around each others, but also to move a tab into a new window) has been broken in the Firefox 8 (Beta) version I use. That was not a Firefox fault, but a problem with the great Tab Mix Plus add-on.
The solution for this was to install Tab Mix Plus Dev-Build 0.3.8.7pre.110917a, a preview development version.
Futher information and download at Tab Mix Plus Forums.
// Updated 20111019:
The Development Channel lets you test an experimental new version of this add-on before it’s released to the general public. Once you install the development version, you will continue to get updates from this channel.
Install development version