One of the strongest arguments against the legalization of gay marriage is that once the traditional definition of marriage has been abandoned, the same claims made for gay marriage can and will be made for any combination of individuals, human or otherwise. "Marriage" will then cease to have any practical meaning except as a way to direct benefits to the "married" group. This process is already going on in Canada and Europe, where polygamous marriage, particularly among Muslims, is already de facto accepted for the purposes of welfare and other benefits.
One new variation which had not previously come to my attention is the "triad", which differs from tradition polygamy in that each of the three individuals is sexually active with both of the other two. Of course, there is no reason to limit such an arrangement to three, but this article describes one such group which is, of course, determined to obtain its rights to "all those survivor and visitation rights and tax breaks and everything like that.”
Advocates for gay rights usually assert that theirs is a special case, and that extension of marriage to gay couples won't lead to an effectively unlimited definition of marriage, but the same courts that buy the discrimination argument in favor of gay marriage will not likely want to discriminate against triads, or any other "oppressed" group.
Extending the example of the polar bear, which is being used as a lever to control CO2 emissions, one could imagine the extension of marriage to groups including people and animals being used to give animals all the legal rights of human beings, a goal of some in the animal rights movement. Get ready for vegetarianism - until someone marries a tomato.