I'm replacing some outdoor lights. The old ones were metal, and the earth wire was connected to a screw on the base. The new fixtures are plastic, and there's no earthing screw. Where should I connect the earthing conductor when installing the new fixtures?
When connecting a fixture in a plastic box, the bare ground (earth) wire is connected to the bare or green conductor of the fixture or a metal screw on the fixture itself. If for some reason you have a very old fixture with no bare or green ground wire, opt for buying a new fixture rather than leaving the source ground wire not connected.
If the new fixture is listed and new, just leave the earth wire not connected. This is perfectly fine, especially since the manufacturers got the fixture listed to be installed this way. We wire smoke detectors this way ALL the time.
If the box is metal you must leave the earth connected to the box.