Travel and running enthusiast Kyle Cash wrote on his blog that the answer to the question depends on how comfortable you are either with or without underwear. Although running shorts with undergarments built into them are made so that you can skip pulling on a separate pair before you head out, for some people the extra material can become uncomfortable because of chafing. " Underwear helps by lowering contact between skin and material," explained Cash. "Plus, the added support can help you feel better. And, for men, adding a little support (and coverage) is always a good idea."
Maintaining a safe distance between any fluids you could be secreting and your running shorts is also a good reason to pull on some undies. You'd be reducing your laundry load each week too by not throwing five different pairs of soiled running shorts into the pile (via Advnture).
On the other hand, if you want to reduce the layers so you feel cooler, keep your genital region clean by preventing extra moisture buildup in underwear, and even look better running (without embarrassing panty-lines), going commando might be your answer. Plus, underwear can ride up and get wedged between your cheeks and this could become uncomfortable too. The best solution is to try running with and without to see what fits you best.