Slacktivist has an interesting and from the comment thread controversial analogy. Somebody in the comment thread mentioned that one problem with Le Guin's story is that she never explains why the child's suffering is necessary. I'm not sure that's true, but when I use this story in my ethics class (as part of the discussion of utilitarianism) I pair it with part of Huxley's Brave New World. The savage insists that suffering and evil must be part of the world if there is to be nobility and greatness (students also often say this when discussion of God and the problem of evil comes up). If there is anything to this, then surely that's the reason the child must suffer; without the child, Omelas would have no suffering or evil, and would perhaps become like Mustafa Mond's world.
To speculate further, perhaps the reason Omelas is such a paradise is that people are much better at ignoring widespread suffering and evil than at ignoring it in individual cases, so the fact that in Omelas it is only this one child who suffers such an unfair fate increases the impact of the example on the people of the city, so that they are inspired to greatness far beyond that which the people of our world are capable of.