Islam allows a man to marry up to four wives, but only one husband for a woman.
A Swiss woman was recently detained for bigamy in Egypt (Reuter, Feb 5, 1997). The article says : "Bigamy is illegal in Switzerland for both men and women. Islam, the official religion of Egypt, allows men to marry up to four wives but does not offer the same option for women."
In the Star (English paper in Malaysia), 22 Oct 96, it was reported that in Selangor, Malaysia, regulations are introduced to expedite the application of man for polygamy without the consent of their wives. The Jabatan Agama Islam Selangor argued that polygamy is a right of the male and the regulation was to make this right accessible.
Others have argued that polygamy is not a right but a responsibility based on an-Nisa' 4:3 and an-Nisa' 4:129. As such, some others have claimed that the Qur'an argues in favor of monogamy. Of course the question remains, why would a law be given that was not meant to be kept?
Judaistic practice also permits polygamy. Mishnah Sanhedrin 2,4 permits the king to have 18 wives; it is not expressively stated how many wives an ordinary man could have, but there are references to four wives (eg. Ketuboth 10,5) and five wives (Ketuboth 3,7). The Qumran community as revealed by the Dead Sea Scrolls forbids polygamy except for the king.
Recommended reading
Polygamy in the Quran is a short, introductory article that gives an overview over a number of aspects of this topic.
This article further explains why Christians do not accept polygamy.
For a more thorough analysis of polygamy in the Quran, go to this online booklet and click on Chapter 12.
See this article on the number of wives and human sexual property Muhammad allowed himself.