What sorts of legal and social ramifications would arise from legalizing polygamy?

I have often wondered why polygamy is so frowned upon in the United States. Yes, I know that it is against Christian values but what about those of us who are not Christian? The way I see it, polygamy is not a morally bad thing, it just involves a slightly different set of morals.

But, this question is not about the moral ramifications of legalizing polygamy, it is about the social and legal ramifications. So, what does the collective think would happen if polygamy was legalized in the United States?