A friend explained that the following is a simple way to test an alternator to see if it is working:
To be clear, I am not recommending trying this.
Will this work? Will it damage the vehicle at all? Is it dangerous to do?
To directly answer this question, no it won't work and you run the risk of damaging your alternator if it is good while doing so.
The test you are asking about was used quite successfully with generators, but should not be used with alternators. Alternators are internally regulated. When you pull the battery lead, you run the risk of killing the regulator.
I'm not saying the car will or will not die with out the battery hooked up. It more than likely will run if the alternator is producing some semblance of juice. Besides the possible damage to a good alternator, if the alternator is not producing full voltage, but just enough to keep the engine running, you'll never know it using this method. If you lose a single diode, the alternator would behave in just this manor.
As pointed out by @tlhIngan, use a multimeter to test the alternator.
Here is a link to a very weird, but good video of how to test an alternator.
EDIT:
Because there has been so much conjecture and comments thrown in below this answer, I'm adding some stuff from what appears to be an authoritative web source. The source is Troubleshooters.com under the section called Automotive Troubleshooting. Here are some excerpts on why you should not remove the connection to your battery with the engine running (I think it pretty much regurgitates what @JasonC says in the comments, but I'll throw it out here anyway):
Your battery does more than just provide electricity. It also shorts AC, spikes and transients to ground. Removing the battery from the circuit allows those spikes and transients to travel around, endangering every semiconductor circuit in your car. The ECU, the speed sensitive steering, the memory seat adjustments, the cruise control, and even the car's stereo.
Even if your computers and stereo remain intact, in a great many cases removing the battery burns out the diodes in the alternator, necessitating a new alternator. If disconnecting the battery interferes with the voltage regulator's control voltage input, it's possible for the alternator voltage to go way over the top (I've heard some say hundreds of volts), frying everything.
Even the initial premise was wrong. If you disconnect the battery and the car conks out, you don't know if it conked out due to insufficient alternator current, or whether the resulting transients caused your ECU (the car's computer, which controls fuel mixture, timing, and much more) to spit out bad data, shutting down the car.
Nobody should EVER run your engine without a battery.
And yet when you tell them not to, they'll roll their eyes. "I'm a professional. I do this every day. It's fine!" They'll sound so authoritative. So commanding. So in charge. So intimidating. But they're wrong.
The problem, of course, is that disconnecting the battery doesn't always damage something. It does it only sometimes. Less experienced jump start professionals and automotive technicians figure if they got away with it a few times, it must be OK.
Here's an easier and safer way to test an alternator.
The method posted by OP for testing an ALTERNATOR will likely destroy perfectly good parts of you vehicle, not the least of which being the alternator. This method should never be attempted in a computer controlled vehicle (basically any vehicle after the 70s). The proper way to test an alternators function is by performing what is known as a "full field" test. This basically involves bypassing the regulator while the engine is running by jumping the field terminal to ground. The procedure is different for different vehicles, but when you do this you basically call for 100% power from the alternator. You can perform this test very briefly without risking damage to anything in the vehicle and test for charging voltage. Once you have done it enough, you can actually simply jump it with a screwdriver and listen for the alternator to start "singing" (it will whine very distinctly when you perform this test if it's working properly). The method of checking for a charging voltage at the battery is normally sufficient and a much better idea for the layman, but to perform the test properly you should do a full field test.
I've witnessed a very simple lawnmower/tractor run this way (as the battery was dead) - once jump-started, the battery was removed and the basic combined starter/generator continued to run the engine.
As others have stated, by contrast with a generator, the alternator is designed exclusively to recharge the battery. In modern cars, the alternator is actually disabled when the battery is full and the electronics will run from the battery for a while, reducing load on the engine and improving fuel economy. The alternator is therefore not designed to run the engine directly, and running it without a battery to handle burst current draw could fry the regulator. Use a multimeter.
