I love hats! I have a long face, large head, and very thick hair so brim/crown proportions are key for me. I often have to wear mens' hats to find the right fit. I don't like any that add height to my already-long head, so low-profile hats work best.
For summer, I have a rancher style sun hat (find #1) that I like, and am on the hunt for one with a larger brim. I also have a couple of low-profile ball caps that I like, on hot days when I need to keep my hair off of my neck.
For winter, I like beanies - but they have to be slouchy or poofy in the back (find #2) , otherwise I look like I have a pencil for a head.
I would love to find a floppy, low-crown, woven hat for summer (similar to find #3) or generously cut wool panama hat (similar to find #4)...