This article provides a good summary of the historical and current practices within Christianity regarding head coverings.
Basically for large portions of Christianity wearing some kind of head covering before the 20th century was the norm, even for Protestants:
Among the Protestant reformers, Martin Luther's wife, Katherine, wore a headcovering in public worship and John Knox and John Calvin both called for women to wear headcoverings in public worship. Other commentators who have advocated headcovering during public worship include John Gill, Charles Spurgeon, Matthew Henry, A. R. Fausset, A. T. Robertson, Harry A. Ironside and Charles Caldwell Ryrie. In fact, until the 20th century no Reformed theologian taught against head coverings for women in public worship. While Anabaptists, Amish, and Mennonites advocate the wearing of headcoverings at all times, as a woman might pray or prophesy at any time, the Reformed teaching is that "praying and prophesying" refers to the activities taking place in public worship, as the Apostle Paul is dealing with public worship issues in 1st Corinthians, chapter.
For current practice:
Headcovering, at least during worship services, is still promoted or required in a few denominations and among the more traditional Catholics.Among these are Catholics who live a plain life and are known as Plain Catholics. Some Anabaptist denominations, including the Amish, Old Order Mennonite and Conservative Mennonites, the Old German Baptist Brethren, the Hutterites, and the Apostolic Christian Church; some Pentecostal churches, such as the Church of Our Lord Jesus Christ of the Apostolic Faith, The Pentecostal Mission, the Deeper Christian Life Ministry, and the Christian Congregation in the United States; the Plymouth Brethren; and the more conservative Scottish Presbyterian and Dutch Reformed churches. Though most Protestant denominations have no official expectation that women cover, some individuals choose to practice headcovering according to their understanding of 1 Corinthians 11.
However to properly understand this phenomena of changing practices I think it is necessary to understand Paul's literal teaching. There is both a cultural and natural basis that explains both the submission to the rule and its abandonment. To Paul one should become 'a Jew to a Jew and Gentile to a Gentile', therefore if a given culture communicated submission to her husband by wearing a purple cone on her head, a Christian woman in that culture should also wear a purple cone on her head.
Let's look at the Apostles meaning, this well then explain why in many churches this practice has ceased.
Bible times regarding head dress were not that different than various places in the Middle East today, where the social meaning is the same (or similar) as it was at the time of Christ. One must realize woman should keep their head covered in these places otherwise it is seen as a huge protests against a woman's submission to her husband. To do so while praying would almost seem like blasphemy.
However what complicates the issue is when Paul argued this case against some sort of biblical radical 'feminists' who were ready to throw away the authority of men under the new changes of the gospel, he appealed to nature.
Does not the very nature of things teach you that if a man has long hair, it is a disgrace to him, but that if a woman has long hair, it is her glory? For long hair is given to her as a covering. (1 Corinthians 11:14-15, NIV)
I believe we must accept the scripture everywhere without forcing the language and then handle the 'damage' to our own ideas after the fact, as well as resolve any seeming contradictions without twisting the original statements. Therefore, I think Paul is now referring to something here that is 'not cultural'.
The way I accept this unchanging rule, while opposing the enforcement of the cultural rule, only relevant in the Middle East, is this way. First, Paul in referring to nature is simply pointing out what most people realize. In general men look silly with long hair (with some exceptions) and in general women look beautiful with long, flowing, gorgeous hair (with some exceptions). Nobody would ever be able to deny this, just looked at models in magazines. Why is this the case? Paul argues it is a natural symbol that shows a woman under the headship of the man. In a man's case his headship is not in this world but invisible, so when praying to God the open air is a better symbol. Not that a woman does not ultimately have Christ as her head as well but that she came from the man, i.e. wo-man, as symbols of societies organization from the original template of Adam and Eve.
Now, I would never imagine for a minute that Paul intended to refer to the natural observation to become legalistic, so that a woman can't be bald in modern day, if she chooses, or that a man can't have long hair and play in a christian rock band, or try out for a Jesus movie, where for some odd reason Jesus is depicted as having long hair. Rather, as a bald woman was a great cultural shame back then, and that not keeping her head covered was interpreted as rebellion, the natural images of nature should not at all be rebelled against. That was Paul's argument. Why rebel against a cultural ceremony if it even has some support in nature? However, once a culture no longer has that meaning, the natural element of beauty is purely a personal matter. Really its about looking good for the opposite sex, or what takes the least amount of time to get ready in the morning, or suits your career image, etc.
Even God did not always follow his own natural symbolism, therefore neither do we need to as a matter of law. For example, the Nazirite was instructed to go against this symbolism as a revised symbol of his 'dedication'. Interestingly his hair may have possibly become a symbol of Christ in the flesh, for when it became large it may represented his 'head' on top of his own head, whereby his 'commitment' actually became part of the fellowship offering. Whenever something is burned in offering to God, it is reasonable for us to draw imagery of Christ in the flesh.
“‘Then at the entrance to the tent of meeting, the Nazirite must shave off the hair that symbolizes their dedication. They are to take the hair and put it in the fire that is under the sacrifice of the fellowship offering. (Numbers 6:18, NIV)
Therefore in the Bible an open airy head may indicate the headship of God as the divine Christ, yet long hair could be the human manifestation of Christ.
Today in most countries we can do whatever we please, even die our hair purple or green and no particular cultural message is being communicated that would be necessarily offensive to Paul. The natural order of things no longer has a direct ceremonial and cultural significance as it once had for most countries.
This explains why the practice for many has been abrogated. There was no Biblical command inaugurating it, but while a culture communicated its values with this symbolism, there was no reason to oppose it. Now that many cultures do not put much weight on outward appearance in terms of the male-female role, there is no reason to oppose to forms of cultural communication. If Christianity attached undue importance to clothing than it could be argued that men should wear tunics and sandals to pay respect to Christ's culture.