Since the Earth has a magnetic field, can it, in theory, be run through a conductive metal coil to create electricity?
Not really. A magnetic field alone doesn't create electricity. A changing magnetic field does. The Earth's magnetic field does change a tiny bit but not enough to really generate much.
The other option is to move the inductor in the magnetic field. The Earth's magnetic field is quite homogeneous over short distances though so the coil would need to move fast and very far to generate much. This would use more energy than it creates (at least on the surface of the Earth).
Several years back there was an experiment (the Space Tether Experiment) to drag a conductor through the Earth's magnetic field with the Space Shuttle. I don't know how viable this is though because I think it saps orbital energy.
Actually, it's possible to use the Earth's magnetic field to generate electricity. A satellite in the form of large diameter loop in orbit around the Earth will generate a current in that loop, and could be used to power something, but at the cost of a rapidly degrading orbit. On the other hand, solar panels creating a current in that same loop could boost the satellite into a higher orbit.
Transferring power out of an orbiting system of this type to somewhere else , and the technical issues involving superconductors are large.
Another way is to use fluctuations caused by solar flare coronal masses impacting on the Earth's magnetosphere, which give rise to magnetic storms. These can induce large currents in long conductors such as power grids. However, they are far more destructive than useful.
On a more practical note, if you could turn the magnetic field of the Earth into electricity you would barely get a year's worth of supply from it before it faded out, given global electricity consumption.
I've been thinking about this lately but I think that u missed something you all are saying that much energy will be needed to make the coil spin I've an objection on this it depends on the shape of the coil and its position also material used. I think if the coil was made to be wide and not long and just flought horizontal away enough from the earth surface at the equator and kept rotating horizontally u won't need much energy to keep it rotating and as far as u go farther than the magnetic source distance between magnetic flux lines will increase so variation in magnetic flux denisty will be achieved easier and using wide coil will increase contact points decrease average weight and decrease its electric resistance.