I spent an afternoon with the widow of a B-29 pilot, who flew with the 20th Air Force in the Pacific Theater. Walter was the Co-Pilot of the "Ancient Mariner" ("Z Square 53").
She let me sort through many of her husband's books and then she told me an interesting story.
It turns out the whole deal about eating your carrots to improve your eyesight was actually operational deception to cover for the fact that the Norden bomb sight had been placed in service. So long as the enemy believed our aircrews just had eagle eyes from eating many carrots, then they'd not realize there was a piece of equipment they needed to place on their capture and exploit plans. Just think, it was such a good plan that it has hung on all these years in the common knowledge data base of parents and those trying to get that little advantage hunting or flying.
Moral of the story: You can tell your mom you won't see any better if you eat your carrots....nor any worse if you don't.
Update on Vegtable Mythology - 3/7/2006: I had breakfast with my friend, Jim, Sr and told him this story. He said they were sort of force fed carrots as pilots, and also said he didn't have much need for a Norden Bomb Sight, so he was never in on the plan to confuse the enemies of Democracy.