Not about the movie.
In a commercial on the tube for Flight of the Phoenix the propeller comes off, outruns the plane, and plows into the fewsalage. (You spell it, please ;))
What would actually happen if a prop did “unscrew” itself?
I’ve seen what happens when the wheel detaches from a race car. Same thing?
Becha Johnny LA knows this one. 
Peace,
mangeorge
At constant speed the propellor is exerting a force forward and the drag of the plane is exerting an equal force backward. What do you think would happen?
Of course, the propellor probably wouldn’t rotate in a stable manner for very long because unless it is alligned perfectly with the airstream there are unequal forces on the blades and I don’t see how it could stay so aligned indefinitely.
They can and do go in most any direction.
Under power, they usually go fwd and any of 360 degrees perpendicular to the crankshaft.
With power removed, they usually slip back past the engine and do a lot of damage to the structure as they go by.
In movies, it is much better to have it saw into the fuselage for dramatic effect. ( which sometimes happens)
I read a first-person account of someone whose prop detached from their plane - he said it went forward and down, after which he lost track of it because he had to get ready for a power-off landing.
But GusNSpot is right - if they’re under power the tendency is to go forward, but once they’re loose they won’t continue in a straight line for very long. Depending on the construction of the airplane, hitting the fuselage is at least a possibility.
On a larger plane, the prop is going to be constant-speed. Which suggests a couple of things:
-
the props are independently attached to the hub. It’s much more likely that a blade will come off than that the whole assembly will come out.
-
If the entire assembly came off, it would lose hydraulics and the blade would go flat, which would cause them to immediately become a source of drag and they wouldn’t go forwards.
At least, I think that’s what would happen.
True, but you can’t rule out a fatigue failure of the prop shaft or crankshaft, which would liberate the entire prop, hub and all.
Dunno for sure, but the C-119 may have had counterweighted blades, not (pilot-controllable) hydraulic props. Those wouldn’t necessarily “know” of a shaft failure. Even hydraulic ones wouldn’t change pitch immediately; after a failure they’d still have thrust-producing pitch for a short period, and that’s all it takes.
A liberated prop will tend to go more downward than in any direction just because of its own weight, but it could go anywhere, even up. Its only source of stability is its own gyroscopic effect, but its moment of inertia in any tipping direction would be so small that it wouldn’t be stable for long.
So the OP answer is “Yes, it’s physically possible, and that’s more than Hollywood will usually give you, so shut up and smile.”
Actually, mr. smartypants, I stated at the top that I wasn’t interested in the movie (hollywood) aspect of what might happen, but in the physics. But the physics part is being pretty well answered. By others. 
At the instant the prop parts with the engine it loses 3500hp of energy, but also loses the equivalent load. All that’s left is the inertia and mass of the prop, and drag, right?
So why doesn’t the prop stay on the shaft and auto-gyro? The energy must be a little ahead of the load, but why?
Immediately after the shaft failure, the prop is still spinning just as fast as before, except it doesn’t have to drag an airplane behind it. Suddenly bereft of a load, its angular velocity will increase along with its forward velocity - it will pull forward and speed up. In effect, it does auto-gyro as you suggest, losing its energy to air friction and/or solid objects it encounters on the way.
The prop will stay on the shaft, the bit of it that’s left after it breaks (the only way the movie scenario can happen is with a shaft failure).