I have a "crusher" hat that looks very much like the one above, and in cooler weather I wear a baseball cap.
My family calls my crusher hat my "safari hat" and they tell me I'm only allowed to wear it in Animal Kingdom. But I wear it everywhere as I am very fair-skinned and I would rather look a little silly than get burned.
Edited to add: Here's a link to my hat:
http://www.duluthtrading.com/store/mens/mens-accessories/hats-and-caps-for-men/40038.aspx It's great because it keeps the sun off your neck, it's very cool and you can roll it up and stuff it in your pocket while on a ride, then take it out and it pops back into shape. I've had mine for about 5-6 years and it still pops like new. I wear the men's one but they have since come out with a more feminine version. (Come to think of it- maybe my family would like it better if I got the girly one?)