An Italian university recently did a study on the best way to stay dry while it's raining. Their findings are published in the European Journal of Physics and state that it really depends on the situation.
When the rain is falling straight down (or on top of you) or at angle towards you, your best bet is to run as fast as you can. If the rain is falling from behind you at an angle you should run at the same pace as the wind, which should be slower than your fastest pace, but you'll still be running.
If its a complete downpour, you best bet is to actually walk! With the increased rainfall rate you can't really outrun any droplets, but also since the ground can't absorb the rain that quickly, as you run the water will slash back up on you. This will, of course, get you wetter that you were before.
The best option over all is to carry an umbrella!!