Robert Baratheon, Eddard Stark, Jamie Lannister, Tywin Lannister... What do all of these characters have in common? Power and strength. These are the guys who have the guts, the glory, and/or the gold.
Arya Stark, Tyrion Lannister, Jon Snow, Daenerys Targaryen... Here are the underdogs. They don't have the strength, they don't have the political clout, and most of them have been pretty poorly treated by those who are supposed to support them - like Daenerys being sold off by her brother for the promise of an army.
I love the way Martin draws these characters because they're both extreme, and balanced, which is no small feat. Robert Baratheon, the conquering hero, has everything. He's got the gorgeous wife, a whole kingdom, a life of luxury, and Eddard Stark, the strong and loyal friend. The only problem is that for every strength, he's got a matched weakness. His gorgeous wife hates his guts and is having an affair, the kingdom sits on the brink of unrest, and Robert's love of the physical pleasures of life prove his undoing.
Eddard, well, Eddard was doomed from the start. He was too honest, too just, too fair to survive in the cuthroat world he got tossed into. A little more political savvy, a little bit of manipulation, and maybe he would have gotten out alive. But, if he had done those things, he wouldn't be Ned Stark. His best qualities proved to be his doom.
On the underdog side, let's talk about Arya. Arya was instantly one of my favorite characters. The little girl with a little sword. Hardly anyone takes her seriously. She doesn't have much physical strength, she's a young girl, she's very much her father's daughter, and once Ned is executed, she's in an incredibly vulnerable position. And yet... Arya is a scrapper. What she lacks in other areas, she makes up for in pure force of will. This is one determined gal and those who cross her better watch their backs.
Tyrion, portrayed excellently by Peter Dinklage, has an obvious physical disadvantage. His father, as a result, treats him with disdain. Everywhere he turns, Tyrion is underestimated, mocked, and ignored. People are constantly blowing him off. The only thing he really has on his side is the family money. Oh, and his razor sharp mind. By turns callous and compassionate, Tyrion pays attention to what others miss and those who underestimate him pay the price, including his father.
In Martin's world, the characters with the most obvious strength often have the biggest vulnerabilities and those with the most obvious disadvantages turn out to be the characters whose good side I'd most definitely want to be on. This balance means that although the world is larger than life and run through with magic, the characters stay real. Like real life, nothing, and no one, is black and white. So, we can't help it if, every now and then, we root for the "bad" guy or find ourselves apalled by the "good" guy. We also can't help it if, as we read, who we consider to be the "good guys" vs. the "bad guys" changes.
It keeps things interesting. It keeps us turning pages (or watching episodes).