According to the many believers, yes. Theres lots of good reading available on the net about the affect of the moons on various wildlife. In short, human generally work on the sunrise and sunset for our body clock. Other animals work on moonrise and moonset or a combination of both. The best time for fishing (and possibly hunting) are 1/2 hour either side of moonrise. And if you add another six hours to this then also fish an hour either side of that time which is when the moon is directly above or below you. Of course this is but just one of many factors and your target has to be there in the first place.
Note that the moons affect the tides so fishing at these times will also have your around the low /high tide mark. You will also find that preferences vary between species so a bit of trial and error and tracking your results will help you work out when is best. But for now, I'm on the moon bandwagon and plan my fishing accordingly.