The reverse also works: should you manage to create a rotating magnetic field, an electrical current will be induced through that rotation. Curl the fingers of your right hand around the magnetic field in the direction it's rotating, and your thumb will approve of the direction in which the electrical current is being induced. Again, just like driving a screw. Hooray for electromagnetism!
Another kind of reverse also works. If you run an electrical current in a spiral, say with a coiled wire, a magnetic field is induced. Inside the coil, the right-hand rule is followed, and outside the coil, the force lines resemble a convection current. This principle is exploited in transformers (of substation fame, not Cybertron), where a third kind of reverse is employed: a coil of wire with electrical current running through it is wrapped around an iron ring, and the magnetic field induced in the iron ring then induces electrical current in a coiled wire wrapped around the opposite side.
Even cooler, you can pass a magnet through a coil of wire to induce an electrical current in that wire. Store that electrical energy in a capacitor, and you've created one of those battery-free shake-lights. Put it in a soccer ball, and you've got sOccket, bringing electricity to people who live without electrical grids!
The sOccket was invented by four classy ladies at Harvard, and I can't believe that nobody thought of this before. But it's great because in about fifteen minutes of kicking a ball around, you can build up enough electricity to power an LED for three hours. That may not sound like much - my rear LED bike light has run off a single AA cell for months - but when you consider that these folks currently rely on kerosene lamps, it suddenly makes a whole lot of sense.
You know what else makes a whole lot of sense? Exercise equipment as electrical generators. Turn your sedentary-lifestyle-inducing office into a gym! But I digress. One of the marketing gimmicks they're considering for the sOccket is "buy one, give one" so you can use your affluent first-world purchasing power to help improve circumstances in the third world. I'd rather just donate two, since I haven't played soccer in years, but I'm sure I can figure out some way to do that as well.
You can read more about the right-hand rule at Right-Angle Circuitry, or AC Electronics for Alien Minds (found via the xkcd blog).