LadyStyx and Iggy asked why a baby born on December 21st is considered lucky, and I started to answer it in the comments section, but for one thing it would have made quite a long comment, and for another I thought they'd see it better if it had its own post.
Many people believe that a baby born on the Winter Solstice (which occurs around the 21st of December) has a strong connection to the spirits. How you view the spirits depends on what your beliefs are. Some view them/it as some sort of God, others view it as nature (i.e. the spirits inside trees, etc) and still others just refer to it as - as Iggy pointed out - as having the ability to see "the little people." But however you look at it, a child born at the time of the Winter Solstice is considered to be able to attune with the spirits, which is - in some cultures - considered to be a wonderful gift... Hence the child being considered lucky.
I'm not 100% sure where it comes from, but I believe - if I'm not mistaken - it dates back to when holy men and women were believed to talk to spirits and ask them for guidance, etc. I could be wrong that it comes from that, but it makes sence and is based on a simular sort of belief. After all, it was the ability to attune or communicate with the spirits that made these men and women holy in their cultures.
The "lucky baby" thing is also said to apply to babies who are born on the Summer Solstice (June 21st) and on Samhain/Halloween. Especially Samhain, when the "veil" between this world and the world of the spirits is believed to be at its thinnest and communication between the living and the spirits (in the sense already mentioned as well as the spirits of those who have passed on) is considered to be easiest.
Hope that answers your question.