Do you get wetter if you run or walk through the rain?
The simplest answer is it depends on the rain, but if we assume that the rain is falling constantly and is falling straight down and you don't change shape as you walk, you will get wetter if you walk.
This is because the rain can hit you in two ways, it can hit all your horizontal surfaces by just falling on them, or it can hit your front by you walking into it. If there is no wind, the amount of rain that hits you on the front is just dependent on the amount of space you walk though, so how far you walk. If we assume that this is a constant the only thing that will change is the amount of rain that actually falls on your horizontal surfaces which is just dependent on how long you are in the rain for, so running probably does make sense.
Of course in the real world everything is a bit more complex, if there is a wind moving with you it may pay to move a little slower as you can get to where you are going without walking though any rain, just have it fall on your head by walking at the same speed as the wind.
Also if you are in a very short thunder shower that will finish quickly it may pay to move slowly during the shower as you won't run into any rain while it is at it's heaviest.
Although I still think in general running is your best strategy, unless you trip up and twist your ankle...