I stumbled across this on Snopes.com while I was looking something else up.
http://www.snopes.com/food/ingredient/carrots.asp
In summary the reason the myth about carrots being good for your eyes was started was as a way to hide the British development of RADAR. They instead told everyone that they could spot the Nazi planes so far out because their gunners were eating lots of carrots.
That is perhaps one of the coolest stories behind an urban legend I have ever heard.