I have seen the generator that produces electricity from the earth's magnetic field demonstrated I have a video if it working It was taken approximately 15 years ago in California
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Two points. First, if you spin a coil in the Earth's field it will generate electricity just like any other generator using a magnetic field. Second, even if you could somehow extract energy directly from the field the most you could get out before the field collapsed is about 10^19 Joules. Since the USA generates around 1TW it could keep America powered for about a year before Earth was left with no field. Even if you could do it, it would be a bad idea.
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$\begingroup$ You're simply calculating $\frac{1}{2\,\mu_0}\,|\vec{B}|^2$ and multiplying by a suitable volume to get your $10^{19}{\rm J}$, right? I'm not sure that this works though: wouldn't the liquid core flow keep replenishing the field, in which case you would be sapping the Earth's rotational kinetic energy (which would keep us powered for a great deal of time)? Might be a good idea to add to your last line the fact that our magnetic field shields our atmosphere from the Solar wind, and thus is essential to keeping the Earth livable. $\endgroup$ Commented Nov 19, 2014 at 9:14