The following information does not apply to baseball caps, trucker hats, beanies with twirly propellers, most cowgirl hats, some fedoras, or anything Rastafarian.
Also, rain hats, ski hats, and fur hats, for outdoor weather protection, fall into a different category.
Note:
Many headwear customs vary from country to country, so investigate dress codes and conventions before traveling to unknown parts of the world. When in doubt, remain flexible and follow what other women do.