Original or UV Buff and/or:
-Nike breathable golf cap: for when I want a brim. Also worn in wet weather under poncho or rain jacket's hood, to keep rain out of my face.
-Columbia Bora Bora Booney: for extensive exposure to direct sun, particularly on the water.
-UnderArmour Arctic Beanie II: for below freezing in camp, hiking in the teens, sleeping when pushing the temp limits of a sleeping bag with layers.
Other headgear:
-Native Eyewear polarized sunglasses: any time the sun is shining, except maybe hiking under heavy tree cover, and usually even then.
-S2S headnet: for when the gnats or mosquitoes are really bad(always when night hiking in warm weather).
-Headlamp: Zebralight H30W for backpacking and general use, Surefire Minimus Vision for "serious" use(planned night hiking, etc)
-Petzl Elios: hybrid helmet for some stuff that I dabble, or want to dabble, in.