Does a full moon bring bad luck?

Almost definitely not. This claim is probably just an urban legend or superstition from times were humans worshipped celestial bodies.

A lot of people believe this, however, and make claims such as "There are more hospital admissions during the full moon" and "The moon effects the tides, so it can effect humans since we are mostly water". These aren't true, hospital admissions do not alter significantly based on lunar cycles and the moon is too far away to effect such small amounts of water as present in the human body. In fact, your computer and chair are exerting more gravity on you right now than the moon is, or ever could really.

So, no, the full moon does not bring you bad luck.