Places like Pandagon, Feministe, and Dr. Science Knows have been talking about the possibility of decriminalizing polygamy, and after reading all the comment threads, I am not convinced that the reasons for keeping polygamy illegal outweigh the reasons for decriminalization.
First, there are the nonreasons being brought up for the criminalization of polygamy - namely those involving the crimes of one Warren Jeffs. Jeffs is the famous Utah polygamist whose community enforces things like child marriage, incest, statutory rape, and all sorts of other bad things that are either out and out illegal or a good reason to change the law so that they are illegal. (That is, a 14-year-old age of consent for marriage is really indefensible.) I am not making excuses for Jeffs and his ilk here - they're misogynistic backwards yokels, and deserve the legal punishment that's coming to them. What I am saying is that these are not reasons for polygamy to be illegal. Polygamy as practiced in this country often goes along with these abuses, but incest and statutory rape are already illegal, after all.
We see a lot of domestic violence and rape and absusive control in traditional monogamist marriage, but as I am going to argue is the case with polygamist marriage, that's all the more reason for the legal institution of marriage to survive. I've touched on this before, but it bears repeating that marriage introduces regulation and arbitration into the inherent issues of property rights and asset distribution in a two-person relationship. If one partner wishes to leave a ten-year relationship where ten years' accumulated property and monetary assets have been shared, the divorce process can help ensure that they get out with something that approximates their contribution (monetary or no) to the household in the last ten years. Those who are not married and face opposition to their leaving the union have no such legal protections, and could well find themselves leaving with absolutely nothing.
The same is true for a wife of a polygamist who is not legally married to her husband. If she wants to leave, or if he dies, she has no legal claim to the assets that were part of the extralegal union. In other words, if polygamist marriage were legal, so too would polygamist divorce be. Otherwise, we're leaving these women - who are already likely to be in abusive or controlling relationships - to twist in the wind of their spouses and "sister-wives."
The objection to the legal complications that polygamous marriage would create has a lot more merit, but I have a hard time believing that they're insurmountable. See here for some suggestions as to how to tease out the legal complications of polygamist/polyamorous marriage.