Leo G, if you assume the islanders were all dropped off on the island on the same day and given the instruction to leave if they have blue eyes, you would be correct. Most versions of the puzzle leave this ambiguous, but for the puzzle to make sense we have to assume that the islanders have no memory of exactly when they came to be on the island.
Even though everyone already knows everyone knows (etc) that at least one person has blue eyes, on the day after the announcement everyone knows everyone knows (etc) that no one left the island that day, therefore everyone knows everyone knows (etc) there must be at least two people with blue eyes, and this continues every day until everyone with blue eyes deduces that there must be one more blue-eyed person on the island than the number he counted and at that point all the blue-eyed people leave.
Followup to: Belief in Belief
One of those insights that made me sit upright and say "Aha!" From The Uncredible Hallq:
The power of real deception - outright lies - is easy for even us nerds to understand.
The notion of a lie that the other person knows is a lie, seems very odd at first. Up until I read the Hallq's explanation of Pinker, I had thought in terms of people suppressing uncomfortable thoughts: "If it isn't said out loud, I don't have to deal with it."
Like the friends of a terminal patient, whose disease has progressed to a stage that - if you look it up online - turns out to be nearly universally fatal. So the friends gather around, and wish the patient best hopes for their medical treatment. No one says, "Well, we all know you're going to die; and now it's too late for you to get life insurance and sign up for cryonics. I hope it isn't too painful; let me know if you want me to smuggle you a heroin overdose."
So even that is possible for a nerd to understand - in terms of, as Vassar puts it, thinking of non-nerds as defective nerds...
But the notion of a lie that the other person knows is a lie, but they aren't sure that you know they know it's a lie, and so the social situation occupies a different state from common knowledge...
I think that's the closest I've ever seen life get to imitating a Raymond Smullyan logic puzzle.
Added: Richard quotes Nagel on a further purpose of mutual hypocrisy: preventing an issue from rising to the level where it must be publicly acknowledged and dealt with, because common ground on that issue is not easily available.