I asked 10 Eagle Scouts what was the best backpacking hat to get and 9 of them recommended the OR Sombriolet.  So that's what I bought.

Yes it's twice the cost of other hats, but it's worth the price.  It folds down the less than the size of a deck of cards, it's waterproof, it's very adjustable, it breaths, it sheds rain.  It's just a very light weight, easy to travel with hat.