How can I fix my leaking tap?

I have on a few occasions had to replace the taps in my flat and the time has come again. I have done as I always have, removed the tap head and valve and bought exactly the same ones. I have installed them but when I come to turn the water on the tap runs even though they are tightly turned off. When I turn them on the water flos faster. How can I fix this so when they are off they are off? Please help