While a dripping tap may not be the most annoying issue, people are often surprised by how much water can be used/wasted by a simple drip and over the course of a month this can push your water bill up.
With older style taps (the ones you screw in and out to open/close), the leak is usually caused by the washed perishing over time – as the tap gets harder to stop, its natural to turn it tighter, which eventually ruins the washer. Most old style taps can have the washers replaced with ease.
In the case of a shower, sink or basin mixer, the leak either indicates that the seals around the spout are old and cracked or that the internal cartridge has started to wear in places allowing water through the gaps. Depending on the brand, these parts can be sourced and replaced by a plumber.
Toilets have two key components; the flush valve and the inlet valve. Both typically have a rubber washer, which like all things will fail over time. If your toilet keeps dribbling into the bowl after each flush, this could mean that the inlet valve is leaking (and in turn overflowing the cistern) or it could be that the flush valve washer is no longer re sealing to hold the water in the cistern correctly.