The one thing I never, ever hike without is a wide-brimmed floppy hat. I need the brim to keep the glare out of my eyes and the top to keep my bald spot from getting scalded.
This is approximately the model I have, from Outdoor Research. It’s light, packable, reasonably rugged and easily laundered back into a condition worthy of leaving in the house.
OR also makes a “Seattle Sombrero” that I happen to own as well. The Seattle version is a Gore-Tex-lined rain hat that does kinda/sorta keep the head dry until you work up any kind of a sweat — which is inevitable because it doesn’t breathe worth a hoot. But it is handy to have around during the rainy season as long as you don’t do anything athletic.
I see a lot of backpackers wearing those hats that drape down to your shoulders — I can see how they’d be more practical than slathering on sunscreen constantly. I admire the folks who don’t mind spending big bucks for a cowboy hat they’re going to get all sweaty and nasty on the trail, but I guess I’m too practical to go that route. But they do look dashing.
There’s not a whole lot more to say about hats, I suppose, but whatever you’ve got, be sure to share with the group.