John: John will wait it out. Depending on how steamed you are at him, he'll keep his distance for the rest of the day, and then attempt at apologizing later on.
Paul: Paul hates fighting with you. And once you've walked away, he instantly regrets what he said or did. So he'll go to his room, and write a song for you, to apologize for what happened.
George: It might take George a while to gather up the courage to actually apologize to you, if he's done something really bad he'll either wait for you to talk to him or beg for your forgiveness.
Ringo: How can you stay mad at Ringo? When worst comes to worst, Ringo apologizes and pretty much forces you to forgive him. He'll do whatever it takes for you to forget about what happened. Get on his knees, buy you flowers, cry, anything.