There are many different types of hats out there but the one that's not really cool but tends to be the most practical for running in my experience are visors. Why? Because they keep the sun out of your eyes, the sweat from getting into your eyes, the rain out of your face and it keeps your head nice and cool because it's not an enclosed top.
I was actually running a couple years before I discovered the magic of a visor and I'm sad that took me so long to figure it out. It is such a wonderful tour of the rain and sun I highly recommend it to any runner who doesn't want to give up a run because it's too sunny or because it's too rainy. Work is just a great tool to keep the sweat from pouring into your eyes Junior long hot runs. I say after my experience it is a must-have in your running wardrobe.
Definitely keep this in mind when you're out buying your next piece of running gear.
Merry Christmas and Keep on Running.