I've heard from multiple sources -- a simple google search will confirm -- that significantly more babies are born during full moon periods.
Are there any studies supporting or disputing the purported relationship between births and lunar cycles?
A skepdic article references meta-research after 100 studies, finding no evidence of any correlation between lunar-cycle and a lot of things, amongst them birth-rate.
(It goes on to explain why the myth might be still around, if you are interested in that sort of thing ;) )
There is other research also: for instance this study1 that is quite clear in its results and conclusion:
The analyses revealed no significant correlates of birth rate.
Although there exists a popular belief that the phase of the lunar cycle and weather conditions affect birth rate, no such evidence was found in this study.
I believe more studies can be found, but this is convincing enough for me.
Neil deGrasse Tyson talked about this at TAM6. Basically, in a few areas there is a slight rise in birthrate during full moons, but, since the human gestation period is precisely 10 times the time between full Moons, that just means that conception happened on a full Moon, and there are certain, romantic, effects of a full Moon…