Ragnar actually had three marriages (in legend, that is: the exact truthfulness of the details of his existence cannot be proven). His first was to Lagertha, a Danish shield maiden. In the history written by Saxo Grammaticus, Lagertha got Ragnar's attention when she dressed as a man to fight against the Swedes who had killed King Siward of Norway. They married and had a son and two daughters.
Ragnar divorced her, however, so that he could marry Thora Borgarhjortr, the daughter of King Herraudr of Sweden. Despite that betrayal, Lagertha came to his aid when he dealt with a civil war in Denmark.*
Even later, Ragnar supposedly married Aslaug, who was the daughter of Sigurd (who killed Fafnir the Dragon in the Nibelungenlied) and Brunhild the Valkyrie. (It gets a little more mythical than usual here.)
Ragnar became a scourge of England and France. The invasion and pillaging of Paris on 28 March 845 is attributed to him.
King Aelle of Northumbria (who died on 21 March 867) was one of the English that Ragnar annoyed. Aelle captured Ragnar and threw him in a pit of snakes. This would have happened prior to 865: the Anglo-Saxon Chronicle for 865 states that the Great Heathen Army that invaded England was led by Ragnar's sons to avenge their father.
*On the TV show, the marriage between Ragnar and Lagertha didn't survive the first season; the writers had him take up directly with the seductive Aslaug, skipping over the more likely marriage to Thora.
