If you've got an old light fixture in an area where you don't need a light, and you don't want anything there, you'll have to cap off the circuit. This means sealing off the wiring in the electrical box to which the fixture was attached so the wires are still live but aren't powering anything, and aren't a danger. Some fixtures lie at a circuit's end point, so you can just cap them off, while other wires allow the electricity to flow to another outlet, in which case you must make the connections to continue the circuit.
Turn off the power to the fixture at the fuse box. Lower the existing fixture off the wall or ceiling by taking out the mounting screws holding it to the electrical box, exposing the wiring behind it.
Snip the wires with wire cutters, freeing the fixture completely and leaving the wires hanging out of the box.
Strip off about ¼ inch of insulation from the end of each of the wires, using your wire cutters.
Twist a wire nut over the end of each wire, covering the exposed portion completely. If there are two wires of the same colour (meaning the circuit continues on past the electric box, to another box), then twist the nut over both the like-coloured wires at once, holding them side by the side and pointing in the same direction.
Wrap electrical tape around each of the wire nuts and partway onto the wire itself, sealing them completely.
Tuck the wires into the box, making sure the ends aren't positioned directly against one another.
Set the box cover over the front of the box and secure the cover with the screws that came with it. Turn the power back on.
Never work on any electrical system without cutting power at the fuse box.