From what I can tell, the HBO character Ragnar Lothbrok (Or Lodbrok, depending on the language, which means Hairy Breeches)... their actually not really sure if he existed or not, considering that he married the daughter of two of the most famous mythological characters in Nordic... well, mythology, Sirgurd (guy who killed a dragon or something) and Brynhildr, queen of the Valkyrie. It's also guessed that he is legendary because many of the famous things that he has done have been attributed to a couple other major Nordic kings of the same era.

That said, he is guessed to have lived sometime between 800 and 1000 A.D.

As for the reasons why Vikings went a-viking, it's very simple. During the summer, best time to be doing their raiding, most of the farms are... well, during the summer, there isn't much to do one farms, and the men can be spared, and since the men can't go to war against their neighboring Earls without the king's permission, they need to find elsewhere to go if they want to fight. Besides the obvious (greed, taking gold and goods from poorly defended monasteries and fishing villages), it was considered more honorable to go out and raid, pillage and overall end lives than sit at home. So, a grand mixture of greed, honor and cultural reasons mixed in. At least, that's what I figure out from what I've read. They never really made much of a thing about Christians killing pagans. Never really had much of a grudge against Christians, feeling like it was beneath them to hate the weaklings and whatever. The only times that they actually attacked in revenge was when a great chieftain was killed (Ironically, Ragnar's sons sailed with the largest fleet ever assembled of vikings to attack England after Ragnar was executed.)