What can stick to a magnet but does not conduct electricity?
a black rock
Whether or not a magnet can conduct electricity depends entirley on the material of which they are composed. If its a metal magnet, then more than likely, albeit poorly. A magnet can CREATE electricity, by inducing movement in the electrons of a copper wire, as you can see in a generator (copper wire coiled into a cylinder with magnets moving perpendicular to the coil)
Assuming you mean electrical conductor / insulator, most bar magnets are made of solid metal, either iron, neodymium or an alloy of aluminium nickel and cobalt, so they conduct electricity. There is one type of magnet called a ferrite magnet which does not conduct electricity - they are the type often found in loudspeakers.
Metals can be used as wire because they have the ability to conduct electricity, or allow for the movement of electrons from one atom to the next. While some metals are magnetic (have the ability to "stick" to a magnet) and some are not--magnetism is not the variable that dictates whether or not a metal is a good conductor of electricity.
Volt Metre is the apparatus used to detect the electricity generated. Moving a magnet in or around coil of enamelled copper wire or vice versa will generate electricity. The electricity generated can be detected, by connecting the ends of wires of coil to a Volt Metre. The Voltage generated proportional to the speed of movement and strength of the magnet, and the number of turns of the coil.
Some magnets conduct electricity quite well. Others are pretty good insulators. If the magnet is made from metal, chances are that it will be a pretty good electrical conductor. If it is a ceramic magnet or one where magnetic particles are suspended in a non-conductive medium (like those flexible rubber fridge magnets that businesses like to distribute) then the magnet will usually be a very poor electrical conductor.