The veil is not a uniquely Islamic convention; the practice has a long history in the Judeo-Christian tradition. Catholic nuns engage in the practice, of course, and there are several references to the practice in both the Old and New Testaments (King James Version). Ironically, the representation of veiling in the Bible is much more problematic than those in the Qur'an or the Hadith, because the Judeo-Christian sources imply that women should be covered because of their inherent inferiority. I Corinthians 11 (3-10) offers one example:

But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God. Every man praying or prophesying having his head covered, dishonoreth his head. But every woman that prayeth or prophesieth with her head uncovered dishonoreth her head: for that is even all one as if she were shaven. For if the woman be not covered, let her also be shorn or shaven; but if it be a hame for a woman to be shorn or shaven, let her be covered. For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man. For the man is not of the woman; but the woman of the man. For this cause ought the woman to have power on her head because of the angels.
For more information about veiling in the Judeo-Christian Tradition. Among Muslim women, the debate about hijab takes many forms. Many believe that the veil is a way to secure personal liberty in a world that objectifies women. Several women have argued that hijab allows them freedom of movement and control of their bodies. Understood in such terms, hijab protects women from the male gaze and allows them to become autonomous subjects. Others have argued that the veil only provides the illusion of protection and serves to absolve men of the responsibility for controlling their behavior.

Both positions assert that Islam is not responsible for sexism. In fact, the Qur'an supports the notion of gender equality. As scholar Fatima Mernissi puts it "the existing inequality does not rest on an ideological or biological theory of women's inferiority, but the outcome of specific social institutions designed to restrain her power" (Beyond xvi).

Mernissi views the recent rise of women's repression in some Muslim countries as a rejection of colonial influence:
The fact that Western colonizers took over the paternalistic defense of the Muslim woman's lot characterized any changes in her condition as concessions to the colonizer. Since the external aspects of women's liberation, for example, the neglect of the veil for western dress, were often emulations of Western women, women's liberation was readily identified as succumbing to foreign influences (Ibid, vii).
Although written in the 70's, Mernissi's work sheds light on more recent events like the reinstitution of mandatory veiling by Afghanistan's Taliban regime.
For more information about veiling in the Judeo-Christian Tradition, see Women in Islam Versus Women in the Judeo-Christian Tradition: The Myth and the Reality by Dr. Sherif Abdel Azeem.