I think that the idea is that the windpipe is being crushed when someone is being choked in the movies. It only takes a few seconds to do this, you won't die in 30 seconds but after about three minutes you would be brain dead. Without immediate medical intervention, a crushed windpipe is quickly fatal.

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No you would not die though you may lose consciousness. In the movies the guy doing the choking gives a little twist which is supposed to break the victim's neck. That's not very likely either but don't try it at home you could do some serious damage twisting someones neck. Also most of the choke holds you see in the movie would not damage the wind pipe as most of the force is on the sides of the throat which temporarily cuts off the blood flow through the jugular vein and the oxygen supply to the brain causing the temporary unconsciousness. Often you are still able to breath while in a choke hold but because there is no oxygen available to the brain.
As someone previously mentioned the damage to the larynx from choking, this could definitely occur in cases where someone is being choked from the front using there hands. Though I think in this case the blood flow and oxygen may still be getting to the brain so the victim may not lose consciousness as quickly, but after a few minutes with no air the victim will die.

The above answers shed much light on this interesting question about how fast you would die after being choked like in the movies. Yes, if your lungs aren't inhaling air with oxygen in it, after several minutes, your brain will start to die, your heart will go into cardiac arrest, and your prospects for surviving get progressively worse.

There are several swiftly applied countermeasures that could save a life after a trachea is crushed, :

1. Do an emergency tracheotomy by stabbing into the trachea with a sharp instrument (pen, pencil, knife, anything that can make a useable hole with minimal further deformation of the trachea), at the front of the neck below the crushed area, so that the victim can inhale through a hole below the trachea and resume breathing. But make sure your thrust is into the trachea and does not damage an artery going to the brain! Hopefullly, someone with medical training nearby will do that for you, but if you're the only one for miles, you have to decide fast what you will do.

2. The other would be to apply rescue breathing and hope that you can establish even a small air passage. Even a small volume of air getting to the lungs can make the difference between life and a fast death.

3. The third would be if there is a way to fast-chill the victim. People who fall through frozen lakes and technically drown have been revived many minutes later, if the cold water around them slows down their metabolism to the point of being in a temporary state of suspended animation. If this is the road taken, get 9-1-1 help immediately. Every minute counts while the body is so chilled, and eventually even a very slow progressive brain damage will start killing the victim's brain, which will certainly affect what shape they will be in when and if they recover.

And the advice to get to 9-1-1 ASAP applies to #1 and #2 as well, of course, since the damage to the victim from the choking may be more widespread than is observable from just looking at the victim.

A crushed trachea is a serious injury and is usually lethal, so any application of first aid would be a last-ditch every-second-counts desperate effort to save the life.