What's that dripping sound I hear in the attic whenever we turn on the water?
Sounds like a pipe expanding or contracting to me.  When the water runs through the pipes (even the drains), the temperature change causes the pipes to move.  Usually where they are passing through a wood surface, you'll hear an occasional sound, not unlike a drip, that will stop when the pipe reaches it's final temperature.

If the sound coincides with the hot water reaching the fixture (or extra cold water from outside in the winter) then you shouldn't have anything to worry about.