Suppose you're driving down the freeway one day. As you're about to take the exit, you tap on the brakes -- and you don't slow down. No matter how hard you press, nothing happens. You have no brakes! What are you going to do?
When you press on the brake pedal in almost all cars today, you're pushing on a piston. That piston pushes on brake fluid in the master cylinder, pressurizing the brake fluid. It flows through thin pipes, called brake lines, to pistons at each wheel. Those pistons apply pressure to the brake pads, and they squeeze against a disk or a drum to stop the car. If you were to have a catastrophic loss of brake fluid or if someone were to cut your brake lines, nothing would happen when you hit the brake pedal.
The first thing to do if you ever find yourself in the "no brakes!" situation is to try pumping the brakes. If your brake lines have a small leak (instead of a cut), you may be able to pump enough fluid into the system to get things under control.
The next thing is to try the emergency brake -- this is definitely an emergency! If someone cut your brake lines, he or she was probably smart enough to cut the cable for the emergency brake as well, so let's say that you find that the emergency break is out of commission too.
Now you officially have a problem. The next thing to try is the transmission. You can downshift a gear at a time and use the engine for braking. Lots of people do this with their manual transmission as a matter of habit. It works just as well with an automatic transmission. Drop to a lower gear, wait for your speed to decrease and then drop down another gear. If there's a grassy median, you can drive onto it to aid the process. The surface of the grass and the uneven ground will provide a little resistance to help slow the car.
If you're doing all this and it looks like you're going to run into something before you get the car stopped, then think strategically. Given a choice between running into something solid -- the massive concrete post of a bridge -- and something that will give way -- a chain link fence -- choose the object that will give way. If you can scrub off speed by edging the side of the car against a wall or a guardrail, that's a good idea. Or, if you can drive up a rising embankment, that will also help.
In other words, if you have time to save the car by using something nondestructive like the transmission or an embankment, use it. If you can't save the car, then save yourself. Do whatever you can to avoid injury to yourself by running into something "soft" or scrubbing off the speed. And if that fails, then relax and hope your airbag is in good shape!