The hot water valve for our washer started leaking after we turned it back on after replacing our washer. It probably hadn't been shut in years. If I keep it shut the leak stops, but if it's open there's a ever slight drip right at the stem.
I have done some work with regular faucets before, but this one is different as it doesn't appear to be screwed on? There's exposed threads but the faucet doesn't appear to be screwed to those. I've also heard of a packing nut that I could tighten, but from the look of it most of the apparatus seems pretty stuck in place.