I don't have a strong preference for either formulation, and I've certainly used both in blog posts and in other contexts. Neither is wrong or offensive, as Eugene notes. But in most contexts, if forced to choose, all else being equal, I opt for gay marriage.
I do so for two reasons. First, "gay" is shorter and thus easier to type than "same-sex" (3 keystrokes versus 8). It's also less clumsy in many applications, especially if you append some qualifier, like "anti-" or "pro-", to the phrase, as often happens when you're keeping score in the debate. The only easier choice would be "SSM", clearly preferable to "GM", which makes it sound like the argument is about an automobile manufacturer. But depending on context SSM can be too au courant and too informal.
Shortness would not be an advantage if you had to sacrifice much clarity to get it. But I don't think you do sacrifice much clarity in this case by opting for "gay marriage." Eugene is probably right that same-sex marriage is descriptively more precise in the sense that two people of the same sex, regardless of their orientation, are united in marriage. But purely as a matter of communicating effectively, I think people understand what you mean by "gay marriage" without getting lost in distinctions about whether the spouses involved might in rare instances be bisexual or the speaker might intend to refer only to two gay men. "Gay" in "gay marriage" refers to the marriage, not to the spouses, who are in a gay marriage regardless of whether they're bisexual. And while "gay" has come to be associated with homosexual men more than homosexual women, in the particular phrase "gay marriage" I think people understand we're talking about two men or two women. These are judgments — sacrificing a bit of clarity to gain a bit of brevity and avoid clunkiness — about which reasonable people can disagree.
There's a second reason why I have a slight preference in most instances for "gay marriage" over "same-sex marriage." The debate is about many things: marriage, tradition, families, morality, religion, public policy. But it is also about gay people. Much — not all — of the opposition to gay marriage arises from deep opposition to homosexuality itself. Much of the support for gay marriage comes from people deeply committed to equality for homosexuals and who see marriage as an important piece of that larger project. Gay people are the ones overwhelmingly affected by the fact that two people of the "same sex" can't marry. In this sense, "same-sex marriage" subsumes them in a debate that is, in very important respects, about them. If you don't believe me, try having a debate with someone about the issue (on either side) without one or both of you making references to homosexuality. The debate is centrally about both gays and about marriage, so "gay marriage" seems the substantively better fit to me.
"Gay marriage" thus captures something about the historical and cultural significance of the debate, about the arguments for and against, that "same-sex marriage" tries to sanitize. As an example of this effort to sanitize, consider the first pro-gay-marriage decision, from the Hawaii Supreme Court in 1993, which actually has a footnote explaining its preference for the term "same-sex marriage" over "homosexual marriage." The footnote ends by observing that "parties to a same-sex marriage could theoretically be either homosexuals or heterosexuals." I always smile when I read that: please, please, this decision really has nothing to do with those people. Casebooks and court decisions ever since usually refer to it as "same-sex marriage."
Interestingly, the preference for "same-sex marriage" is also shared, for very different reasons, by two groups at opposite ends of the debate. On one end, there are ardent opponents of gay marriage who claim that the debate is not about homosexuals at all and who see it as politically unwise to appear to be "anti-gay." On the other end, there are queer theorists and social constructionists who reject even the categories "gay" and "straight." There's no doubt most academics writing in this field prefer "same-sex marriage."
I'm also not sure which way the respective phrases cut politically. It would be interesting to know whether "same-sex marriage" or "gay marriage" draws more opposition in polling questions that are otherwise identical. My hunch, and it's only a hunch, is that "gay marriage" excites somewhat more opposition because it more directly refers to homosexuality.
Mostly I look forward to the day when we simply call it marriage.