Baseball cap in the summer. Gant make some decent ones.
You can get a flat cap to stay on if you get the deeper cut type. See here. It doesn't have to have the flaps.
http://www.lockhatters.co.uk/In cold weather or for long-distance driving with the top down I use a hunter hat. I find the Barbour one is not too heavy compared to the sheepskin flying type.
http://www.barbour.com/mens/hats/fleece-wax/mens-lifestyle/fleece-lined-hunter-hatHaving your ears covered makes long-distance driving with the top down far less tiring in my experience.