Historically, monogamy was much less popular than polygamy (specifically polygyny) Mostly because of European expansion, monogamy is more popular than it was ever before. See article about Polygamy for details.
Note that the term "monogamy" is also used to mean confining a sexual relationship to one other person even in the absence of a legal status of marriage (for example, an unmarried heterosexual couple or a homosexual couple in a jurisdiction that does not recognize marriage between homosexual persons.) Monogamy in this sense is recommended by health professionals discussing safer sex practices.
Monogamy is occasionally used to mean having only one sexual partner during an entire lifetime.
See also: polygamy, concubinage, marriage, polyamory.