As a child Gregor entered a room to find Sandor playing with one of his toys, he held his face into a fire to teach him a lesson. The reason Sandor feels for Sansa is because (much like him) she's a seemingly innocent victim of circumstance, she had nothing to do with the political choices of her father but she's paying the price for them.
Likewise Sandor is a victim of his birth, the nature of his scars and his upbringing mean that everyone sees him as some kind of subhuman animal even though he's really not a bad person, I have him pegged so far as one of the true heroes of the upcoming novels, I believe his empathy for her also comes from overhearing her sing to someone at some stage, he calls her his "little bird" because she's trapped in a guilded cage whereas he's trapped behind his scars. Her innocence won him over when she thanked him for saving Loras Tyrell from Gregor Clegane during the first King's Landing tourney, she was the only one who saw his intervention as anything other than brutality by an animal.
Tv viewers should note that despite his semi-infatuation with Sansa his motivations weren't as pure in the books, when he was overwhelmed psychologically by the flames (in the book the entire river was coated in wildfire and tens of thousands of men were burning) he totally wigged the **** out and was 100% irrational and broken mentally, the last anyone saw of him was when he refused to sally back out the gate and I believe he was excommunicated/banished as a traitor. A result of this was that he had nowhere to go, "home" belongs to Gregor and the south belongs to Joffrey, his only choice was to "rescue" Sansa and effectively sell her back to Robb as a sign of fealty, it doesn't actually happen though, she turns him down because she's terrified of him and he ends up doing the same with Arya instead (by pure chance).
Martins books are rather unique in that his characters depart from the standard convention of "good and evil", as the series evolves it becomes apparent that the vast majority of characters exist in shades of gray rather than the black and white personae that we originally attribute to them.
The Hound and Theon just need someone who loves them for themselves, Jaime just plays the cards that life deals him and tries to do the best by his family, Cersei is damaged by the death of her mother during Tyrion's birth and the separation from her twin. Even Gregor Clegane isn't the monster he appears to be, he has an overactive pituitary gland and since he was a toddler his skull has been slightly too small for the rest of him, his life is lived in eternal shades of agony courtesy of endless blinding headaches which stop him from sleeping and cause his rage and outbursts... he's known for killing men who wake him when he actually manages to sleep and the chemical rush of battle is all that stops the pain