I'm glad I didn't live in the bygone age when you couldn't go into town without wearing a hat. I own a lot of hats (mostly baseball caps), but I don't like wearing them. I have two exceptions: I wear them out in the sun sometimes and out in the rain sometimes.
When I go to baseball games, I'll wear my Giants cap if I know (or think or suspect) that I'll be sitting in the sun. There are so many overhangs at Pacific Bell Park (which is now SBC Park, eck!) that you're not assured of a day in the sun just because you have a ticket. Besides, it's San Francisco. Even in the middle of summer (especially in the middle of summer) when baseball is being played, you can't count on sunshine.
When I'm riding in the ski boat on the lake (and that's always in the middle of summer), I wear a hat. I take it off when we go fast, because otherwise we'd have to double back and fish it out of the lake. But when we're just cruisin' I keep it on. The top of my head doesn't have quite the natural protection it once did, and I don't need it to get burned.
Today I wore a hat. When I waded out to get the mail I wore my nondescript tan Shasta Lake cap with the dusty blue bill. What I needed more than a hat were boots, because it rained all day and the puddles were deep and wide. But a heavy jacket and a hat had to do for protection. I managed to keep my shoes from getting fully soaked.
Winters are mild here on the north coast, so I don't have to worry about the hat problem very often. In fact, by the next time I feel the need to wear one, the one I wore today will probably be dry. It's hanging on the doorknob getting its shape and color back right now.