I have a red square that I want to drag only on the x-axis. I've worked out a simple script, which theoretically should work, but it's not behaving properly. It's a bit hard to explain..the square keeps starting at the wrong position and the stage position seems to be changing so sometimes you can't drag the square all the way to the right...
Glad Marty's solution worked for you, although it is not too efficient (that MouseEvent.MOUSE_MOVE listener is a killer). The problem with your original code was that the rectangle in which you limit the dragging boundaries must be relative to the parent's coordinates. Also, depending on where you have the registration point of your square, you might have to take its width into account, if you don't want any part of it to move out of the stage.
For example, if your red square is directly on the stage, its registration point is located on its centre, and you want to limit the dragging to the whole x-axis of the stage, this will work: