It's not by chance that a crazy person is called a lunatic. That root luna comes from Latin and it means the moon. In the past there was the belief that the moon caused some people to go bonkers. But, as noted above, there is no scientific correlation between the full moon and periods of lunacy or craziness in certain individuals.
This may, however, be a case of self-fulfilling prophecy. If one believes, as people did in the days of yore, that the full moon caused changes in people, like it made them crazy or turned them into werewolves, then when there is a full moon people look closer for examples of craziness in others. In this human zoo we live in, one can always find instances of bizarre behavior, so it's never that hard to find, especially when you are looking for it.
I agree with Cassius: "...The fault, dear Brutus, is not in our stars, But in ourselves..." (for "our stars," insert "the full moon).
One note, however: If, while looking at the full moon one clear evening, your are tempted to think outside of the little life you are living here on Earth and that gets you to contemplate the bigger picture, the much bigger universe that surrounds us in the vast expanses of cold, star-studded blackness and on to the distant galaxies millions of light years away, then if you really start thinking about it, maybe that will make you, at least for that moment of reverie, just a bit luny.
Note on the note above: Exactly as I finished writing the above answer, I heard that little bell telling me that I had a new email. It was from a site I subscribe to, spaceweather.com. Here's what the email said:
Friday night's full Moon is the biggest and brightest full Moon of the year. It's a "perigee Moon," as much as 14% wider and 30% brighter than other full Moons you'll see later in 2010.
How creepy is that?
Here's something also to be noted (but not so creepy):
Mars is having a close encounter with Earth, and on that Friday night, Jan. 29th, it will join the Moon for an all-night-long conjunction. Don't miss it!
People have long believed that the full moon has an impact on people's behavior. Even today, people will say that students get more "squirrely" when the moon is full.
However, it is not at all clear whether the moon really does have an affect on human behavior. Scientists have done a number of studies of various indicators of behavior to see if there is a correlation. In some cases, there seems to be a correlation, in others, there does not.
Please follow the link for a really excellent page that lists a huge number of studies and then provides (bottom of the page) a nice, understandable discussion of the overall results.