Loyalty is the one characteristic no main character can afford to lack. I think it's the one that readers value most highly. Even anti-heroes such as Hannibal Lecter display loyalty. And the real bad guys are usually the ones who should be loyal - to their friends, to their country, to their cause - and yet sell out.
What I loved about Toy Story 3 is the way Woody is conflicted. He loves Andy, and Andy is loyal to him: he's going to take Woody away to college with him, but leave the other toys safe in the attic. The other toys, not unnaturally, want to be played with and loved. They want to go elsewhere. Woody has a big conflict here: he wants to stay loyal to the group AND loyally go away to college with Andy. He will have to choose...
It's a great situation. Both options are "good" options, but he can't do both. The conflict drives the story. Sometimes he makes a choice, but circumstances draw him back to make the choice again. There isn't a right choice, and a wrong choice - both options involve someone getting hurt. It's a fabulous conflict, applicable in many situations. Superman has it - does he save the earth, or Lois Lane? Or Alec Leamas in John le Carre's The Spy Who Came In From the Cold, who must choose between personal loyalty and loyalty to his country.
Often for the conflict to be resolved the writer must find a third way. Woody's conflict is resolved at the end in a very satisfying way, and so is Alec Leamas' although it has a very different feel. But what has kept us gripped is the big decision - which should they choose? Which would you choose?