The faster the liquid is moving, the less likely it is to drip. If you're pouring, say, from a mug into a pot, just dump it out, and hope it doesn't all splash out. If you can't reasonably dump it out, tilt the cup as much as you can, so that the liquid will move faster.
Always pour from a height.
Hold the container which contains the liquid approximately 10 cms high above the empty container into which you are pouring it.
Tilt it quickly
Tilt the container containing the liquid quickly when you start pouring it. This will prevent the liquid from dripping along it's sides.
Use a spoon as a guide, if required
Hold a long handled spoon vertically in the centre of the empty container into which you want to pour the liquid with one hand. Using the other hand, gently start pouring the liquid along the handle of the spoon, so that the liquid will slide down the handle and fill the empty container.
My mom pours water from her mug into her teapot by pouring it toward herself. Oddly enough, it works - no spills.
Some background on 'why does it drip so much':
This depends on the shape of the rim. A mug usually has a thick, rounded rim. The liquid tends to adhere to the mug and goes around the corner and down the outside of the mug.
A coffee pot is usually from thinner material, so it has a sharper rim and the liquid tends to let go.
The material used to make the container also plays a role. I have a steel teapot with a very sharp rim that always makes a mess. Another teapot (glass) never drips.