Eventually all taps drip. It's fate, like toast falling butter side down. The traditional style of tap forms a seal using a ring of rubber screwed down onto the end of the metal feed pipe. In time the rubber, either becomes brittle and splits, or just wears through and it will then no longer properly seal. If the washer is not replaced immediately, water seeping through the gap will erode the valve seat. The choice then is to either, replace the tap, or re-grind the valve seat, assuming of course, that you have a valve seat re-grinder handy. Not good either way. But, these days there is now an alternative. Ceramic disc taps.