But not if they move to Alabama or North Carolina. You would be well served to read the opinion - it specifically allows the *each state* to decide marriage in a manner binding upon the federal government. The most cogent arguments are made not by the majority, but by the dissenters, which point out, among other things, that this precedent would allow couples formerly considered married to lose that status if they moved to a state which did not recognize them as married.
A marriage is organized around extending to others the very same gift of life they received from their parents. A gay couple, by their choice, avoids even the possibility of having children.
As a state provides for itself by taxing the incomes of people, it would better serve its own interests to encourage the former arrangement and discourage the latter. While there are many arguments in favor of traditional marriage, the fact that a traditional marriage is arranged for the material interests of the state is all the justification needed for a state to define marriage as the union of one man and one woman. The religious, civil, and social aspects of this arrangement can be completely irrelevant. Likewise, what DOMA did was codify the definition of marriage for the sake of government efficiency and uniformity - and believe it or not, judicial precedent considers this reason alone a legitimate reason for a law. There is nothing in the Constitution which would prevent Congress from changing the law to recognize gay couples as married. But they have not done so.
Instead, the Supreme Court has changed the meaning of the law in a way the original authors did not intend. This is a very bad precedent to set in general, but even worse when one recognizes that this ruling makes a law limiting marriage to one man and one woman Constitutionally valid, so long as it is passed at the state level, rather than the federal. How the federal government deals with a surviving spouse who moves to a state where their marriage is considered invalid, we have yet to see. But it seems to me that instead of settling the issue of marriage, the decision today allows for the polarization of the issue along state lines. It further allows for a time in which, after public backlash, the states decide that gay marriage was a mistake, and subsequently invalidate - by legislative fiat - many "gay marriages" - opening the door for the federal government to prosecute for back taxes and denial of government benefits. If the state in which one resides does not consider a couple legally married, from the federal point of view, they are not. And this decision strengthens the state's case, rather than the individual's.
Under this ruling, the partner of a gay soldier from California would be entitled to a surviving spouse pension, whereas one from Alabama would not.
Under this ruling, Utah could allow a man to marry multiple wives, and the federal government would be required to pay a social security pension *to each one of them* upon his death.
However, if the man moved to Illinois before he died, none of his wives would be eligible for a social security pension. Worse, they would all have to pay taxes on his estate because Illinois doesn't recognize polygamy as valid.
From a legal perspective, this is a really bad ruling. There are better ways of changing the law than judicial activism; Congress passed the Civil Rights act of 1964 in a time when racism was still very much a large part of American culture. They did it because it was the right thing to do. But redefining marriage to specifically include immoral relationships is particularly prejudicial against Christians, Jews, and Muslims, and infringes on their rights to live according to their faith. Congress could have chosen to recognize unions other than marriage, or not to recognize it at all, but again, they have not done so. Instead, our laws are being vetted not by our elected representatives, but by appointed judges.
What will happen when, in the opinion of the Supreme Court, gay marriage is unconstitutional? Or an affront to liberty?
Regardless of whether you agree with the outcome or not, this decision came at the cost of our ability to self-govern.