What is the moral of the story After Twenty Years?

One valuable takeaway from O'Henry's "After Twenty Years" is that the past always catches up to you. Bob lives a life of crime, and he thinks all his "hustling around" will never catch up to him. He is in the wrong place at the wrong time, so he is arrested. For keeping his appointment with Jimmy, Bob pays for his crimes. O'Henry seems to be cautioning against doing bad things, as they will always catch up in the end.
Another lesson we learn is not to underestimate anyone. Bob brags about his success and hopes "Jimmy has done half as well. He was kind of a plodder, though, good fellow as he was." Bob is saying that the Jimmy he knew was unambitious, yet he was a good person. He believes that his friend will keep the appointment because Jimmy is reliable, and "he always was the truest, stanchest old chap in the world." So, while Bob trusts Jimmy will come, he does not think Jimmy will have been successful in his life. He certainly never guesses that Jimmy has become a police officer who will have him arrested. The truth is, if Jimmy is so true and such a good person, the only thing he can do is turn in his old friend; Bob does not seem to know Jimmy so well.
Another valuable moral here is that doing the right thing must take precedence over everything else. The two friends keep their twenty-year appointment; that should say something about the value of friendship. However, once Jimmy recognizes that his old friend is a wanted criminal, he must make a choice. He writes to Bob, "Somehow I couldn't do it myself" because he feels guilty for betraying his old friend. It's an understandable feeling. But Jimmy knows the right thing to do is to arrest Bob, so he places the law before a friendship.

It's an interesting question (and be aware that, more widely speaking, there's nothing requiring that any particular story have a moral, and in fact many writers prefer not to assign a clear moral to their work, preferring to look at themes more broadly and ambiguously—leaving the questions open, so to speak). In this story, however, I'd suggest there's a strong focus on the degree to which people can change across the decades, sometimes for the worse. From that perspective, I would say that one moral is to be careful about the kind of choices one would make, because these would have a lifelong impact on one's life as it will follow. In Bob's case, his turn towards a life of crime will ultimately lead him to be arrested within the events of the story.

I believe it would be safe to say that the theme of O. Henry's story "After Twenty Years" is an old one: Crime Does Not Pay. O. Henry contrasts two different characters who have two different philosophies and two different value systems. Bob is greedy and materialistic. He wants to make a lot of money, buy a lot of things, enjoy a life of luxury, and display his success conspicuously. And he doesn't care how he gets the money as long as he gets it. Jimmy is conventional and conservative. He wants a good steady job that is socially useful. He wants a home and a family. The two men's different philosophies take them on different paths until they finally meet again after twenty years. Jimmy has a good steady job that is useful to society. He likes his work and he has security. When he retires, he will receive a pension for the rest of his life. Bob, on the other hand, has made a lot of money through crooked means. Still, he has no home, no family, and no security. The money hasn't really done him much good. He has spent some of it on a scarf pin with a big diamond and a pocket watch decorated with small diamonds. It is important to him to have other people look at him, to admire and envy him. He is always on the run, and it is probably inevitable that he will end up in prison sooner or later. In O. Henry's story, Bob discovers that he can't even trust the man who used to be his best friend. Bob probably has no close friends because he never stays in the same place long enough to acquire friends, and also because he is not the kind of man that decent people would want to have as a friend. His flashy lifestyle has made him conspicuous, easy to identify wherever he goes. His career ends when he is led off to jail. If he has a whole string of crimes charged against him in Chicago and elsewhere in the West, he could be spending a long part of his life in state prisons. Crime really does not pay.
The theme of "Crime Does Not Pay" is also to be found in at least two of O. Henry's other most popular stories, "A Retrieved Reformation" and "The Ransom of Red Chief." In "A Retrieved Reformation," Jimmy Valentine falls in love and plans to get married, but he realizes that his whole shady past has come back to haunt him, regardless of how much money he stole and how highly regarded he might be in the underworld as a professional safe-cracker. In "The Ransom of Red Chief," the two kidnappers are forced to pay to get rid of their victim. O. Henry served time in prison for embezzlement, and he associated with professional criminals after his release. He must have come to realize that crime ultimately catches up with its perpetrators.