Answer:
1. Raindrops that fall on your head and shoulders. These would hit you even if you were standing still. Obviously, the longer you are in the rain, the more raindrops from this category will hit you.
2. Raindrops that you bump into as you move forward. Assuming that the rain is falling fairly constantly, each cubic foot of air in front of you will have roughly the same number of raindrops at any given moment. Because that is fairly constant, we can pretend that those drops are stationary, floating in the air. As you move forward you will bump into them, and you will bump into pretty much the same number of drops regardless of whether you are walking or running.
Looking at it that way, you would get much wetter by walking than by running. That is exactly what experimental testing shows. Running can keep you as much as 50% drier than walking. If you are still not convinced, get some sheets of cardboard and wait for a rainy day. Hold a piece of cardboard flat against your chest, and walk about ten feet through the rain. Getting a new sheet of cardboard, carefully run the same distance. You should be able to count the number of drops on each. Other experimenters have used identical sweat suits with hoods, weighing them before and after each trial. The suit worn while walking always comes out wetter and heavier.
This is only true for when the rain is falling straight down. If the wind is blowing, then a lot depends on whether you are going into the wind, or in the same direction a the wind.