I use an Ultimate Hat, owned it for years and it's still fine. It floats, stays on, folds up small. etc. Just that as my face has got fatter over the years.....the brim is looking smaller!!!
So, I got an Akubra Territory this year ready for my hols. It's got a huge brim on it (4 and a bit inches) and at first I felt like a bit of a berk in it........till I saw everyone elses red necks and bald spots, then I felt rather smug. It kept the sun of both of my chins too. Got it cheap on e-bay as they are quite expensive otherwise. Good hats they are, keep you dry in a downpour, get the right size and they stay on in strong winds too, they can also have a cord attached to them if you want to.
Got another hat on the way from Oz....my mate has found me a genuine Aussie Army slouch hat....£2.80 from a flea market. Should do nicely for the visits to the woods..............all I need to do now is practice my Colnel Bogey whistling.