The answer depends on what assumptions are being made. In the following scenarios, I assume that the wire is light (so its mass can be neglected), flexible (bends with little force), and is so thin that it does not experience significant drag itself.
Airplane moving at constant velocity; no drag
The mass will hang vertically. The only forces on the mass are vertical : gravitational attraction to the Earth and tension in the wire. These forces are balanced. There are no horizontal forces on the hanging mass. If the wire did not hang vertically then there would be a horizontal component of tension in the wire which is not balanced by any other force, so the mass would accelerate forward.
Airplane moving at constant velocity; there is drag
Now there is a horizontal force on the mass, which must be balanced by a horizontal component of tension in the wire. The wire cannot be vertical; it must be inclined.
Airplane moving at constant acceleration; no drag
The hanging mass is accelerating forward, so there must be a net horizontal force on it. This can only be provided by the tension in the wire, which must therefore be inclined to the vertical.
Airplane moving at constant acceleration; there is drag
The horizontal component of tension in the wire must now do 2 things : (1) balance the drag on the hanging mass, and (2) provide enough unbalanced force to accelerate the mass. The wire will hang at an even greater angle to the vertical.