This is a really simple electric motor that only requires some wire, a battery, and a magnet. Simon Quellen Field has a wonderfully detailed description of how to build the motor, and some elegant tips on how you can make the motor run faster.
My middle-schoolers quite enjoyed building one of these, and I’m planning on having my high-school physics students also try it; only a couple of them claim to have done it before. It should be a good way to tie together electricity and magnetism.
(Evil Mad Scientist has an even simpler motor, but, given that the risk that their homopolar motor is quite capable of launching a drywall nail across the room, I think I’d suggest not trying that one without extremely close supervision.)
Although it’s a bit trickier, another great way of demonstrating electromagnetic induction is to build a simple alternating current generator that runs a small light bulb.
Bill Beaty’s website explains how to build the generator in excellent detail.
The best part of building the generator is that you can actually feel the extra energy it takes to light the bulb, as you spin the magnets.