FindMyPast.com, which largely handles British, Irish and Australian records, uses the term "spouse."
MyHeritage.com is an Israeli company that is positioning itself to be the major rival to Ancestry.com. They use the term "partner" for each person in a same-sex married even though partnership is also a relationship option. Hence, regardless of whether one lists the relationship as a marriage or a partnership - it will always display as a partnership in reports, etc. Still, it is an acceptable response.
Oddly, MyHeritage Family Tree Builder, their software that syncs to their online trees, lists my wife and I as "wife" and "wife." Go figure.
RootsMagic 7 allows for the manual selection of labels for both persons in a marriage: for one the label "Father," "Husband," or "Partner" and for the other "Mother," "Wife," or "Partner." It does not seem to have a problem with the person being of the wrong sex of the label. Pretty weird, actually - it must be a fix to a database structural problem that assigns to each marriage a first (male) and second (female) position.
Heredis uses the term "spouse" for each person in a marriage.
Of the various major software progframs, only Legacy 8.0 doesn't allow recording same sex marriages in some form, and although there are work-arounds, the software will "correct" these if the user takes advantage of the error-correction features of the software. (These work-arounds require a entering one spouse as the opposite sex and then changing it afterwards.) This appears to be intrinsic to the data structure of the program, and would need either a major revision to the architecture that I don't see coming until FamilySearch.org comes around, or some weird fix like RootsMagic made.
It would be nice if a single program had all of the features and functionality that I want. Sadly, none quite make it.