Do you have any idea how much water your faucet will use if it is constantly dripping? It depends on the frequency it drips, of course, but a faucet that drips 10 times per minute, which isn’t really all that much, will waste 500 gallons of water in a year. If it drops faster than that, it could easily waste several thousand gallons per year. Even if you live in an area where water doesn’t cost you money, you should still be concerned with wasting a natural resource.
Many times, fixing a dripping faucet isn’t very complicated. It could just be a question of replacing a seal or a gasket. You might not be familiar with how to fix something like that, but with the help of a plumber it should be a quick fix.
In more serious cases, it might be necessary to replace the entire faucet, but this too is not a very complicated process, and purchasing a new faucet is not very expensive.