NetBeans 6.x editors handle double-click differently from other applications. In firefox, thunderbird, eclipse, or even terminal, I can doulble-click anywhere in a word to select the whole word, keep the mouse button pressed, and slide forward to expand the selection.
In NetBeans, doing the same will drag the selected word, just like moving the word elsewhere. While it seems cool to be able to drag-and-drop, I don't see any practical value. In java editor, I always avoid drag-and-drop anything, since the selected element often lands in the wrong place when your mouse/pad reaches its end.
Update: It has been fixed in NetBeans 7.1 according to this bug. I installed 7.1 beta just to get this fix.