I use this Flydanna for running.  It is great for keeping the sun off my head, and the sweat out of my eyes.

The cotton is very thin and lightweight, so it breathes well.  But, being so lightweight, it feels flimsy.  It is not.  I've been using the ZAN flydanna's for over a year now, and they hold up well.  Sure, they do fade with time and washing, but I've had no problems with the durability.