(sorry about not knowing all the names of stuff, the english is not my native tongue)
Depending on the type of the faucet, there's an option for a really cheap and more permanent fix. We had a leaky faucet and each time the 'rubber-part-that-goes-inside-the-faucet-handle' (sorry, don't know the real translation :)) gets replaced, it works for a little while, but after a month or so you just can't turn the faucet hard enough to stop it from leaking.
I'm not sure if that's the problem you're having, but here's what was the problem in our case... the place where the faucet knob/handle goes in, if you unscrew that just like you're preparing to replace the rubber (provided you closed off the water in bathroom), you will see where the rubber on the inside of the handle touches the metal circle. The turning of the knob is what moves the rubber to and from the metal circle, giving the way of water to pass through. The problem here is that if the water is dripping for some time, the metal gets "eaten away" by the water, ie there's a canal going through it's surface, so no matter how hard you turn the knob the water passes through the canal. When you replace it the rubber is more flexible and it can fill in the gap, but after a while it hardens and that's when you need to replace it again.
The only solution here is to take off some of the metal. There's no way you can do it without a proper tool though - there's a special "screw" with metal teeth that you tie instead of the knob, and by turning it like a knob the metal teeth eat away at the metal evenly. That way the metal gets even, and now when you place your original knob it will hold the water in.
Hope it helps.