Polygamy can be defined as a marriage which includes more than two partners. In Westeros for the highborn and the lowborn marriage is chiefly between two people, a man and a woman. The Faith of the Seven does not permit polygamy.
Polygamy in Westeros
House Targaryen was known to flout convention and openly practice polygamous marriages. Aenar Targaryen took multiple wives with him when he left Valyria for Dragonstone. Aegon I Targaryen was married to two women who were also his full sisters, Visenya and Rhaenys. When Aegon married his sisters, this was considered unusual although there was precedent for it.
Aegon's son Maegor is the last Targaryen known to have had multiple wives. His second marriage to Alys Harroway upset the Faith and led king Aenys to exile him to Pentos for a time. With the death of their dragons House Targaryen lost the clout that they needed to be able to get away with committing the sin of polygamy in Westeros. According to George R. R. Martin,
Maegor the Cruel has multiple wives, from lines outside his own, so there was and is precedent. However, the extent to which the Targaryen kings could defy convention, the Faith, and the opinions of the other lords decreased markedly after they no longer had dragons. If you have a dragon, you can have as many wives as you want, and people are less likely to object.
There has been no mention of a Targaryen woman having more than one husband.
In the Iron Islands a man can still have several "salt wives" but only one true ironborn wife, his "rock wife". Salt wives are considered more than mere concubines. Children born of such unions are not considered bastards and can inherit if their father has no surviving sons by his rock wife.
King Garland II "The Bridegroom" Greenhand had multiple wives until he put them aside to marry the daughter of Lymond Hightower. 
Polygamy Beyond the Wall
- Beyond the Wall the wildling Craster has multiple wives, some of whom are also his daughters. Ygon Oldfather has eighteen wives.
Polygamy in Essos
- In Lengii, the first god-empress of the current dynasty, Khiara the Great, took two husbands, one Lengii and one YiTish - a customary pattern followed by her daughters and their daughters in turn.
References and Notes
- The World of Ice & Fire, Aenys I.
- The World of Ice & Fire, The Conquest.
- Chicon 7 Reading (September 02, 2012) So Spake Martin
- The Citadel. "Asshai.com Forum Chat" (July 27, 2008) So Spake Martin
- The World of Ice & Fire, The Reach.
- The World of Ice & Fire, The Stormlands.
- A Dance with Dragons, Chapter 69, Jon XIII.
- A Game of Thrones, Chapter 46, Daenerys V.
- The World of Ice & Fire, Leng.