In the TV-show Vikings the sagas revolve around Ragnar and his sons. I was wondering whether there existed other Vikings who were more famous or conquered more than Ragnar or his sons did. This is excluding Ragnars brother Rollo of course.
As far as modern fame goes, in the English-speaking world it would be tough to surpass Beowulf.
As far as conquest goes, Ragnar appears to have been known mostly for raiding. Cnut the Great however, made himself king of a not inconsiderable empire covering Denmark, England, Norway, and southern Sweden.
The Rus leaders who fought for and won control of the Russian river system from the Baltic down to the Black sea may well have scoffed at Cnut's paltry empire though.
Considering that Ragnar and his sons are figures as much out of legend as of history, I will answer with another legendary figure:
Ivar Vidfamne. According to Snorri, he began in Scania (today the southernmost part of Sweden), and began by conquering the (then much smaller) Swedish kingdom. He then went on conquer "all Denmark, a big part of Saxonia, the whole Eastern kingdom and a fifth of England." Snorri based most of his account on the older poem Ynglingatal, which he also quotes from, but nothing that supports this story.
Ivar is also known from Hervarar saga, which says that after Sweden, "[h]e also subdued Denmark and Courland and the land of the Saxons and Esthonia, and all the eastern realms as far as Russia. He also ruled the land of the Saxons in the West and conquered the part of England which was called Northumbria."
He is further mentioned in a lot of other Norse sources. They all seem to agree on him conquering at least both Sweden and Denmark.
Snorri I have in translation to Swedish by Karl G. Johansson. Hervarar saga I found here. Other primary sources are mentioned by Wikipedia, I checked on Sögubrot (Swedish translation) and Af Upplendinga Konungum.