As a Messianic Jew, let me point out a piece of Jewish tradition that may help shed some light on this issue. In the same verses that Paul directs women to cover their heads in prayer, he also instructs men just as strongly to never cover their heads in prayer. However, Jewish men, today as then, ALWAYS cover their heads when they pray. (in fact, so do women) Consider the traditional "kippah" head covering, that little round ornate piece of cloth that only covers the top of your head, held in place with hair pins. In Yiddish it is sometimes called a "yarmulke" which means "respect for the Sovereign." It is a tool specifically designed for use by men in prayer, and it was probably in common use in the time of Jesus. But going back further than that, to the time of Moses, is the prayer "tallit," a shawl worn by men in more formal prayers at the synagogue or at home (such at the during the Shabbat meal). In lieu of either, any piece of cloth will do; I've even seen people reach for napkins at the dinner table! To a Jew, it is unthinkable, irreverent, strictly forbidden, a sin of the highest order, to come before God in prayer with an uncovered head. Because of this, I think we can safely assume that both our Lord Jesus and the Apostle Paul practiced this "religiously" (since we have no clear statement that they rejected it as false).
What shall we say then? Was Paul a hypocrite? Was he placing demands on others that he himself did not follow? Or did he or someone else address the Jewish practice of head covering in more detail and expel it as false doctrine, and such documents being lost to history? I think the more plausible answer is that Paul is addressing here a more profound meaning than head fashion -- one of the heart. It is the same heart that is expressed by Jews by wearing the kippah: a heart of respect and submission before God.
Today, in our country, what does it mean to take off your hat when you pray? Or when you enter a church, or someone's house? It means respect. What does it mean when you leave your ball-cap on at the dinner table? Disrespect. What does it mean when a woman wears a mini-skirt or a low-cut blouse to church? Disrespect. It is believed that in first century Greece, a woman with loose, flowing, uncovered hair was most probably a prostitute. It was indecent in public, just as it is considered indecent by Muslims today. I think what Paul is saying is don't come to church dressed like a prostitute! Show some respect! Dress and act with appropriate decorum. Both men and women, act with respect! Women, show respect to your husbands, don't dishonor him by parading around in public half naked. Men, show respect and submission to God when you pray and take the leadership role in the home and in church.
In my opinion, this is the true message of this passage, and I think a message that is desperately needed to be emphasized and enforced in our churches today, as it has been apparently lost of many of the young worshipers that I see on Sunday mornings in my church.