Gas ranges use igniters to light the oven and burners. The igniter makes a clicking sound when it generates a spark and lights the burner. In most cases, the igniter stops clicking when the oven or burner lights. In some cases, however, problems in the unit cause the igniter to continuously attempt to light. If this happens, you'll hear a continuous clicking sound.
If excessive water gets into the igniter, the igniter will short out, leading to a nonstop clicking sound. Once the water evaporates, the igniter usually stops clicking. In most cases, this condition isn't dangerous and won't cause permanent damage, but if clicking drives you crazy, you can turn on the oven for 30 minutes to help the water evaporate. Before taking this step, soak up any water in the burners or the oven with a clean cloth.
Dirt or dust in the burners can cause the gas range to constantly click. Clean the burners by sticking a paper clip into the holes and moving it around to dislodge any dirt or debris. Don't use toothpicks to clean the burner. Toothpicks can break inside the burner holes and add to the clicking problem rather than resolving it.
Broken Ignition Switch
If your range continually clicks, your ignition switch may be broken. If the ignition switch breaks, the igniter continues to generate sparks even after the stove or oven is already lit. This leads to a continuous clicking sound. Your service technician can replace the ignition switches for you if they are twisted or broken.
Most issues that cause clicking are not dangerous or permanently harmful to the oven. However, if you hear clicking, you should troubleshoot it and call a technician if necessary. Gas stoves are always potentially hazardous because of the potential for gas leaks -- if anything seems wrong with your stove, you should have it checked right away to make sure it's not dangerous to you.