The best running hats will be your companions on many runs. Photo: iRunFar/Eszter Horanyi While there are endless options for running hats — and choosing the right one can seem like an impossible task — the best running hats have several features that make them stand out from the rest. Hats can shield your face, eyes, scalp, and lips from the sun, keep rain off your face, wick sweat, and keep hair contained.