A magnet thrust into a coil produces a noticable deviation on a table galvanometer. Or the coil can be moved over the magnet. (See also Special Relativity Demonstration)
In another demonstration two large coils are placed adjacent to each other, one connected to the galvanometer. When the other is pulsed with a battery, the induced current will be noted on the meter. You can emphasize the point that a steady current in the primary will induce no current in the secondary. If an iron core is positioned through the two coils, the galvanometer readings will become dramatically larger.
Faraday Bulb
A coil connected to a small bulb is mounted on a disk. When the disk spins the coil through the poles of a magnet, the bulb lights for that part of the arc for which the coil is passing through the magnet.