Amazingly enough, there is a scientific answer to this problem, and it is extremely complex. It depends (I bet you knew that I would say that) upon a number of factors.
Your height, basic shape - these dictate your cross-sectional area.
Your speed - this dictates how long you are out in the rain, but it also alters the angle of the rain relative to you.
Wind speed = this also alters the angle of the rain relative to you
Wind direction = this alters your profile relative to the direction the rain is coming from and consequently affects your cross-sectional area which is presented to the rain.
Raindrop size - this dictates how fast the rain is falling, but not necessarily how much rain is falling.
Rainfall rate (amount of rainfall per hour).
There is no stock answer - sometimes you will get wetter, sometimes you will stay relatively drier, but in general if you can present the smallest cross-sectional area to the direction the rain is coming from, this is going to allow you to remain relatively the driest.
In other words, walk or run at the same speed as the rain in precisely the direction the wind is blowing TO.
I bet you never knew that.
Example - an Olympic sprinter, faced with a 200 metre sprint in a downpour from the wrong direction could be drenched by almost half a litre of water. If he were sprinting in exactly the opposite direction, it would be a mere 50 millilitres (about a good mouthful).
Again, if you want to play, you can find the algorithm by following this link :