Since I keep linking to the new website The Head Covering Movement, because he puts up such good references, I feel I should add that he seems to accept many of the traditional forms of head covering that I have come to reject. I don't think we need to imitate the Mennonites or Orthodox Jewish women in how we cover our heads. There is no need for "snoods" or "kapps" and in fact neither of them really fulfills the requirement as I understand it anyway.
The requirement is for a katakalupto, or down-falling covering such as a shawl or a scarf. If we understand the requirement to apply only to the worship service, as I now do, then a scarf draped around the neck where it can be easily pulled up over the head as we enter the sanctuary seems to me to be the ideal solution. It's simple, it doesn't call attention to us, it's not too susceptible to glory-stealing fashion competitions and so on.
I think a simple sewn beret can be OK, the larger the better for covering head and hair, but not hats, which start to compete for glory in themselves, often don't cover the head anyway, much less the woman's glory, her hair, and easily come to threaten the line of sight of anyone sitting behind them. Witness the hats worn in England, which were probably originally inspired by First Corinthians Eleven.
Just want to be clear that I'm not calling for us to look like Mennonites. Or the Duchess of Cambridge either.