This is a regression in 7u6. The functionality works with 7u5.
Reported with NetBeans - Drag and drop doesn't work. You can't reorganize any tabs in window, either you can't move some selected code to another part or move classes between packages etc...
Evaluation on NetBeans side - The first attempt to drag anything (an internal window or a node in Projects/Files window) actually does start. But after a short time the dragging is interrupted for unknown reasons. The drag rectangle representing the dragged object is still being painted on the screen (on top of all windows). Furthermore, the system Dock becomes disabled and does not react to mouse events - it isn't possible to switch to other windows by clicking their Dock icons. Popup menu on the Dock doesn't work either. Switching to other apps with keyboard works fine though. After quitting the application in broken drag mode, the Dock becomes responsive again. When dragging is interrupted there's still a Thread stuck in DragSourceContextPeer.doDragging().
Not reproduced outside of NetBeans.
Note for JDK team - NetBeans implements its d'n'd support using java.awt.dnd classes, we don't use javax.swing.TransferHandler.