Just to use a widely known example:
Rowling managed to give Snape and even Voldemort sympathetic sides through introducing the bits of their backgrounds that make us understand (1) why Snape is so bitter and (2) that Voldemort is indeed psychopathic, psychically crippled from birth. This program comes to a head in Book 7, when she shows Snape as a child so emotionally deprived that he is "greedy" for friendship and when she gives us the terrible image of Voldemort's shattered soul as a flayed, abandoned infant.
That's the "here's why the jerk became a jerk" method.
Another example is Child and Preston's character Pendergast, an FBI Special Agent whom many other characters consider arrogant and insubordinate, coldly intellectual. However, those characters whom he befriends learn how deeply loyal and loving he can be and how deeply committed to the core ideals of law enforcement.
That's the "you only think he's a jerk because you don't know him" method.
Finally, there's the difference between book-Aragorn and movie-Aragorn. While I have no problem with book-Aragorn (having gotten used to the traditional self-proclamations of similar heroes from Tolkien's model epics), I've heard from many that he strikes them as arrogant. Movie-Aragorn, on the other hand, is shown to have doubts about his ability to fulfil the destiny that pursues him, and it's generally others who proclaim his illustrious ancestory (f.e., Legolas at the Council of Elrond, who tells Boromir that Aragorn is his lord, while Aragorn looks embarrassed at the brouhaha.)
That's the "great as he is, he has self-doubts" method.
Then there's always the ragged mutt method, as mentioned above. Love of animals (or the human downtrodden) seems to redeem difficult characters in many readers' eyes. Examples from Bleak House: I had instant and deep sympathy for the mysterious character Nemo when Jo the street-sweeper said the man always shared his scanty cash and food with him. Ditto Mr. George, who picked up the crippled soldier Phil Squod on the road and kept him under his wing from then on. Also in Bleak House, Miss Flite, who keeps many little birds in her miserable garret as the embodiments of all her long woes and long-delayed hopes.