This article from the Weekly Standard is one of the best things I’ve read answering this question. One of the dangers it convincingly outlines is polyamory.
Among the likeliest effects of gay marriage is to take us down a slippery slope to legalized polygamy and “polyamory” (group marriage). Marriage will be transformed into a variety of relationship contracts, linking two, three, or more individuals (however weakly and temporarily) in every conceivable combination of male and female. A scare scenario? Hardly. The bottom of this slope is visible from where we stand. Advocacy of legalized polygamy is growing. A network of grass-roots organizations seeking legal recognition for group marriage already exists. The cause of legalized group marriage is championed by a powerful faction of family law specialists. Influential legal bodies in both the United States and Canada have presented radical programs of marital reform. Some of these quasi-governmental proposals go so far as to suggest the abolition of marriage. The ideas behind this movement have already achieved surprising influence with a prominent American politician.
Does this sound radical? Read the article and tell me what you think? He has convinced me.