For many people running is a meditative experience. It clears their mind. Others use the time to wrestle with mental issues, perhaps a thorny relationship issue or maybe a problem at work.
Those people are freaks.
Have you ever gone running? It's exhausting! And painful! Trying to solve mental problems while running is like trying to perform calculus while being stabbed in the eye. I suppose it's possible, but doesn't it seem likely that you'd get distracted by the blood spurting out of your retina?
Actually I do perform some simple calculations while I run. At any point during one of my runs I can tell you, with reasonable accuracy, how many miles I've run and how many miles I've got left. I'm constantly calculating and recalculating what percentage of my run is behind me. I guess this is analogous to informing the stabber, "My eyeball is only 62% demolished! 38 to go!"
My current favorite game to play while running is a little bit of excitement I call: Guess How Many Seconds Have Elapsed Since I Last Looked At My Watch. I can say with a great deal of certainty that this is pretty much the most fun I can have while pounding out the miles. Sometimes I let 8 or 9 seconds go by before guessing, other times as much as 90 seconds will elapse before I breathlessly (literally) check my watch to see how good my guess is.
The real fun comes in when I then calculate what percent I'm off by. Then, over the course of the run, I average out those percentages. Wheeeeeeeeeeeeeee! Typically my guesses are off by around 14%. Awesome!
Honest to god, this is the most fun thing I can think of while running.