Polygyny is a form of polygamy where a man has more than one wife at one time. In the United Kingdom, this is illegal.
Institutionalised polygyny is not common but even where it is allowed, it is not commonly practised as few men in such communities have the financial means at hand to support more than one wife. It is usually observed in groups of people that have recently experienced war or famine - disasters which typically kill proportionally more men that women. The Anglican Church in Kenya for example, has semi-officially adapted a positive stance on polygamy, largely because of deficit of males in that country due to decades of war.
Many societies, including some ancient European and aboriginal American, have a tradition where a man is responsible for widowed women in his family and this would often entail an effective or literal marriage even if the man already had a wife.
See Polyamory for the main article on this area.