All known human societies, present and past, have heterosexual marriage: a man and a woman perform a ritual in front of their community and a religious figure or elder, throw a large party with lots of food, and then they go to live toghether and have regular sex, and the community will consider them a family, which entails a number of rights and obligations depending on the local laws and customs.

In many societies a man can marry multiple women, although usually only high status men do it. In very few societies a woman can marry multiple men, usually brothers or cousins. But even in a polygamous marriage the marriage relationship is largely intended to be binary: one party can be married with multiple parties, but these other parties aren't married to each other. They have few mutual rights and obligations and are generally not expected to have sex with each others.

Traditionally, in socieites which accepted homosexuality, there was no equivalent of the marriage relationship for people of the same sex. Homosexual relationships were intended to be pre-marital and extra-marital, occurring aside heterosexual family-building marriage.
Cohabitation and regular sex between unmarried people of the same sex may have been tolerated, but it was not encouraged, and certainly not given social or legal recognition.

Legally and socially recognized homosexual marriage only occurs in some modern Western societies.

EDIT:

Apparently, some ancient societies did give some degree of legal recognition to same-sex unions, although not equivalent to heterosexual marriage: http://en.wikipedia.org/wiki/History_of_same-sex_unions