First Corinthians 11:4-7 seems to imply that women should wear a headdress when attending church services.
1 Corinthians 11:4-7 (NKJV)
4 Every man praying or prophesying, having his head covered, dishonors his head. 5 But every woman who prays or prophesies with her head uncovered dishonors her head, for that is one and the same as if her head were shaved. 6 For if a woman is not covered, let her also be shorn. But if it is shameful for a woman to be shorn or shaved, let her be covered. 7 For a man indeed ought not to cover his head, since he is the image and glory of God; but woman is the glory of man.
Length of Hair – Some suggest these verses deal with the length of the woman’s hair and not necessarily about a headdress. They believe it has to do with a God-ordained distinction between men and women that is to be demonstrated by the respective length of their hair.
Authority – Paul is talking about authority. When we recognize the authority of God over us, we are subjecting ourselves to His authority. Likewise, women wearing the head covering were publically demonstrating their subjection to the authority placed over them.
There is no such custom in the church:
1 Corinthians 11:13-16 (NKJV)
Judge among yourselves. Is it proper for a woman to pray to God with her head uncovered? 14 Does not even nature itself teach you that if a man has long hair, it is a dishonor to him? 15 But if a woman has long hair, it is a glory to her; for her hair is given to her[a] for a covering. 16 But if anyone seems to be contentious, we have no such custom, nor do the churches of God.